Bibliography of Schlicht Functions

S. D. Bernafdi A s \ o c i r r et ' ro l n s \ o ro l \ 4 a l h e n i a l i c( sR e r i r e d l .J.r i.rfl Lr,rcrsrl! ...

Author: S. D. Bernardi

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S. D. Bernafdi A s \ o c i r r et ' ro l n s \ o ro l \ 4 a l h e n i a l i c( sR e r i r e d l .J.r i.rfl

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BIBLIOCRAPHYOF SCHLICHTFUNCTIONS

1965) FART r ( PART U (1966-1975) , PAR.Trrr (1976-1981)

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CONTENTS

PAR]I(

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PARI ll (1966 l9'15) l9ll I ) PART lll ( l9-76_

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CONTENTS

PARTt (

1965).

It (r966lr'r5) PARI'I l l ( 1 9 7 6 l 9 l j l )

lll 211

v1

BIBLIOGRAPHY OF

SCHLICHTzuNCTIONS -1e65) PARTI (

CONTENTS vii I

P:eface. BibliograPltY

Bibliography"" Supplementary

List of MathematicalJournals ' '

PaPers. ExpositorY T o p i cR e f e r e n c e. .3. . . . Co. recltons

" " '

l0r 113 116 117 I JL

PREFACE

tg'l-t o:::it;:,?li.:rl, T;; 1694references Thisbibliographvcontains

lTh*:l,f ::^:"""-"i"1*,:$L ;rm; H:t.*li. lil,**t"'"T'fr iilnu#f llrn,t*il";'ffi and ,ao.,r,r, Iecturenotes'

l*:'l*i'lill"iil'ili; ::i"#ru':'Ji:i::"+i,l*l;".xi::i::ifu ::iffi:*i*h*nui:I $i;;'i *"; t,TxJrff i{:i,::ilffi 'ror"uoo'"*imately the rematr 1400 papers' while ,nu,n' .

uo tiurioe'upt'v Tlfjii:l#;1::l;l':n::*:fi[:l:i]'i:' 'itiinttt or ll'lt"' titles the word univalent t'""i"t" oroximately736 of them

vlll

classof Horvever'*unl:"lttll]: irr the multivalent(or their equivalents) not specifically pJpt" *ttot"'fitle-s-,1ot and schlichtfunction' utt tontutntJ'in iunttiont'!o:*:1' tuntttons' are referto them,'utnu"vp"uifi-ttut theorems.in thesethreeclasses pu'f; rnuny ttut positive of funciions in the classof *tif ft"o*t' into theorems easilytransformed,a'sts

not ;rc lre '"1'::l'-:).:".n''h'."hle "n":::'lli::':,i trrebibriographv analvtic from tontuin

"tit:1;:t-lltt dealingpnmarilv*'itf' uniuatlntv' aremadeby nianywritersof sp"cific'references *nicn to iunctiontheory wereobtit'sunnorlingl references paperson schlichttunctron;'il;;; ii t:nltt-n]'.fl"ctionsand intainedfrom the UlUtrograpli"''tip"ptt' Bieberco"ifitlntt ' -fuUcr-p-olynomials' c'un'tyof treatments clude

i "JuirJ.i, l'",.: ::1,fi:T? ;*;l:li*r;,"$i;:#i.,'111, ;*' orsoruproperties rorms' ;ti'on,roepritz l?li'iilil'XilriiTiLlilffi ;;;;;' tion,nf theclifferential

"tti,+ritli"Ltf

rl.tttlrXli'jll orthogonaltraJectorres' ,i.ti""ii"., tott"ricalderivative' theory tt"ier who is f amiliarwith the quadraticdif ferentialib'rnt ift" ' toplcs of these therele''r-ancy recognize '""dily *'rr functions alent of unir. in the iitriogtuptty [52J]appeared Thc earliestpupt' ri'*tiln"rtt *"the l"r, 1965(withthesingie latest the o";.rr;;;.";.; and 1902, vear * veart96o) Koebe'spaper[688]' oi [i ii] *iiich exception "o;;;;'i; givingthefirstactualresultln in 1907'rsgtntt"lt:]"*utaetias published functtons' of univalent ihe theor,r' in beenreviewed tttitjjt 'rtt bibliography papers flve' fur Mathematik ivlostoi the ;rr ttt" z*tialblatt the Nlathernatictlntu'"o (FM)' and rotittrtti'tt derMathematik (Zbl) or in the Jahrbuch"il;;; theendof each "ii'il'"t 'iti'-1"ii* ondpownu'n.ii) iherotume ::!:'^:!3!,.* reviewnumbers' " rsOrefcrences^lacking referenceof tnt upp'o*tiluteiy technical aslecturenotes,dissertations, mostof themmay oecrassifieri recemtoo or papersnot vetpublished' colloquiums' ;;;;;;.,;it"otrts, in the Reviews' iv puLtitt.,tfor inclusion followsthe tu.9 A "suppremen'^"';i;;;;;;li" of "^Trences "j someof the more recently a iist intiuJJ' uno bibhograpnv rnain

erero"uii'r"'rtit::î.li::":;l;:lT :'"TTffi'.';..andtwentv-one, APProximatelYone years during the

Reviews prblished ences were locatedin 'nt''U"ttt' were hun'jred and forty-two references 1940-1964,volumes f-ZS' f*o le31-1953' in tr'" z""rariiatto"uri'ita d1nl:.:f:'vears Iocated lcca-'edin were eighty-one-refueilces volumts l-102' One n'"atta and 3l-63'

il;;;;;-t published theJahrbuch

tqoo-tsrr'volumes

IX

mathematical A volume-by-volumesearchwas made of twenty-two A list of public' journut, *t i.t are readil; availableio the American is contain functionswhich they itr.r. jou.nut, and the paperson schlicht 'vhich are devoted foffo*ing thi: is a list of erpository papers of "1r.". ; puri,o u generalsurvcvcf th: developmentof ihc thcJrv ;;;i1;;; univalentand p-valentfunctions' hove been The vorious resultsin the theory of schlichtfuncticns those into sixty-eighl topics.Eoch tttptcis followed by a list of -rlrjrrlnrrt clossified thol pertoining to inthe bibtiogrophy that contain information the in the topic. M,reover, tt the end of each reference ..bihliograpb' topics the indicaling nimbers enclosedin brackets are topic re.j'erences whichorediscussedin|hereference.Thefoirowingtwoexai',rplesillustratethe principal use of the bibliog:aphy' conjecExa,npieI . Reference[363]tists"A proof of the Bieberbach Schiffer' M' and Garabedian ture for the fourth coefficient," by P' R paper may be The notation MR 17-24 indicatesthat a review of this page24.The numbersin iound in the MathematicalReviews,volume 17, paper containsinformation U.u.f.." 19, 17, . . , 541indicatethat the Functions)'topic regardingtopic T9 (Meiomorphic Urrivalent(p-va^lent) Bounds for the iiz tco!fn.i.nt Bounds), . . . ' topic T54 (Coefficients Class(S)). funcironrple 2. The reader rvho is interestedin close-to-conver ll29' 282'656' ' ' Al43l tions rvill iind thit topic, T5. The references be found, respectiveindicatethat informatiorrregardingthis topic may T G Erzohi' W' tV, in tft. pape:sby e. Sietecldand Z' Le*andowski' bv the letj. suffridg.. Numbersin brackets.preceded ii;pi";, .'. . , r. indicatereferenceto the SupplementaryBibliography' Theclassificationoftheva;iouspirpersintotopicswasbasedona (of the full-length reading of approxirnately five hundred reprints (b'icl) abstractsor the of pup..rj, and in mosl caseson a reading we emphasizethat the i."i.*i. Therefore, in fairnessto the authors' of the papers' classificationsdo not inciicatethe completescope paperpublished It is difficult in a work of this natureto coverevery it is felt that this on the subject of schlicirt functions' However' the publicationsin this iitriogrupiti does include a major portion of field. the aid givenme by.n.rygraduatestudents I gratefullyacknowledge me !'"ilh someof the GeralJBierman and Victor Stanioniswho assisted ambiguousreferences' numeroustasks of filing, tracking down certian a n d t h e t r a n s l a t i o n o f s o m e f o r e i g n p a p e r s . T h e r e p l i e s t o m y take requests gratifying and I for renrints from numerousauthors were indeed

I owe many this opportunity to extend to them my heartfelt thanks. library thanksilso to the most cooperativepersonnelof the mathematics To New York Univerat the Courant Instituteof MathematicalSciences. and Science sity I am indebted for the financial aid given me by the Arts FinalResearchFund that helpedpay the cost of typing the manuscript. ly,Iwishtoexpressmysincereappreciationtothechairmanofmy graciouslyin clepartment,ProfessorF. A. Ficken, who cooperatedmost and convearianging my teachingscheduleso as to give me sufficient nientlntervalsof time to enableme to completethis bibliography' S. D. Bernardi May 1966

r

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS (PART I) J' GakugeiTokushimaUniv' l. Abe, H- A noteon subordinotion' MR 19-401'Ul Nat. Sci.Math 7(1956),47-51' d-omoin'Sugaku a ring-shaped 2. Abe, H. on conformalmannilslf 20-664P' 10' 18' 481 ,2s';;' tiupu"tttl MR 8(1956/s?) J' GakugeiTokushimaUniv' '3. Abe, H. On p-vaienifunctions' 16' 17' 19] 14' a(iqizl, 33-40.MR 20-i05' [9' in on annulus' Kodai Math 4. Abe, H. on 'o^'-oiotytic iunction' 1 0 ' l 3 ' 1 5 '4 8 ' 6 6 1 4 5R' 2 0 - 5 4 4 ' f 2 ' 6 ' S e mR ' e p .1 0 ( 1 9 5 8 ) , 3 8 - M in an urtnulus'Math' Japon' 5. Abe, H. On uniiitent functions 13',15', 17' 25' 2'7' 48' 58] , zs-ig. N',rnzi-zs3' l9', 5(1958/59) d'unefonctionholomorphe N' i)' rc cercled'univalence 6. Abramesco, deuxzerosd'une eqrntion petite distance,entre plus la sur (x) et f [43] 834-836'Zbr4-10' Sti' Paris194(1932)' .f (x) = /. C.R' ;tlO' holomorphe d-'une fonctio^n N' Surle cercled'univalence 7. Abramesco, d'une equation zeros cleux petite distanceentre f (x) et sur la pius Zbl 9-76' 49-s4' --l. Rt;;:"6i"' r'aut'Palermo58(1934)' f (x) t43l

BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

zur Theorieder konformen Abbildung g. Ahlfors,L. (Jntersuchungen Sci' Fenn' A' l(1930)' No' 9 und der gonrcnFunktioien' ActaSoc' FM 56-984. [s9] Picard. c'R. g. Ahlfors, L. Su) une generalisationdu theoremede ' Acad. Sci. Paris lg4(f%D,245-246' Zbl3-407 l59l lemma.Trans.Amer. Math. 10. Ahlfors,L. An exteision'ofschwarz's 371 S o c . 4 3 ( 1 9 3 8 )3,5 9 - 3 6 4Z' b l l 8 - 4 1 0 ' U 9 ' Duke tr{ath' J' l4(194'l)' 11. Ahlfor s, L. BoundedAnatytic Functions. 1-ll. MR 9-24-[37'60] and extremalproblemson com12. Ahlfor s,L. Opei nieminn surfaces 24(1950)' 100-134' pact subregions. Comment' Math' Helvet' MRi2-90. [59i Notes' Oklahoma A'and 13. Ahlfor s, L. Conformal mopping' Lecture , 9 5 1 .[ 5 9 ] M. College1 14.Ahlfors,L.Developmentofthetheoryofconfcrmdlmappingand R i e m a n n s u r f a c e s t | t r o u g h a c e n t u r y . C o n t r i b u t i o n s ! o t h e tMR heoryof No' 30 (1953)'3-13' Riemannsurfaces.a.nn' of Math' Stud'' 1 4 - 1 0 5 0[.5 e ] York' lg53' 247' MR 14-85?' 15. Ahlfors, L. Complex Analysrs'New

t5el 16.Ahlfors,L,ExtremalProblemeinderfunktionenTheorle.Ann. N / i R\ 9 - 8 4 5 ' 1 2 4 ) A c a d . s c i . F e n n .S e r .A . I . N o . 2 4 9 1 ( 1 9 5 8 ) , 9 ' l'7AlJfors,L.;Beurling,A'Invariantsconformesetproblemesextremoux.DixiemeCo-ngresdesMath.scandlnaves'(1946),341-351.

MR e-23.[5e] l S . A h l f o r s , L ' ; B e u r l i n g , A . C o n f o ; . m o l i n v a r i g n t s . a n12-17l' dfunction. t59l Acra Math. g:itqso), l0l-129. MR theoreticnut-sets. Invarianls. constructicn and lg. Ahlfors, L.; Beurling, A. confoimol of a Symposium ; Applications of conlormal Maps, Proceedings Appl' Math' Ser' No' 18' 243-245.Nat. Bureau of Standards' W a s h . ,1 9 5 2 .N I R 1 4 - 8 6 1 '[ 5 9 ] 20.Ahlfors,L.iGrunsky,H.UberdieBlockscheKonstante.Math.Z. 42(1937\,o7t-673' FM 63-300' U9l theorem' Kodai Math Sern' 21. Aikaw a, 3. On extensionof Sciwarz's R e p . 1 9 5 2 ( 1 9 5 2 ) , 1 0 4 - 1 0M6R' l 5 - 2 1 0 ' [ 3 7 ] univalenceof regular func22. Aksentev,L. A. Sufficient conditlonsfor tions.rzu.vvss.uceu,..Zaved.Matematrka(1958),No.3(4)'3-7. (Russian)MR 26-278' [4] 2 3 . A k s c r r t ' e v , L . A . E l e m e n t c r y c r i t e r i a f o r u n i v u l e n cMaiemhtika eintermsof Ucebn', Zaved' boundory charocteristics'lzv' Vyss'

Zbl 96-55'l!'6:r0' 621 No. Oitr),3-8'(Russian) (1959),

24.Aksent,ev,L.A.Integralrepresentationsofunivalentfunctions,

FUNCTIONS (PART I) BIBLIOGRAPHY OF SCHLICHT

3

(1959)'Nc' 4(i 1)' 3 8' (RusIzv. Vyss.Ucebn'Saved'Matematika 231 sian) MR 24A-37 ' 14, 16' ^, partial ---l:^t sums o,,nc /r of powerserrcs' of 25. Aksent'ev,L. ;' d''the'uniialence Izv.V yss.U ce un' At' ed' lviatem atikuit' qOO) ' No' 5( 18) ' 12-15'( R us 43) stnl fvfn 74A-153' 14' 20' 23' dani' (Jnivalentuoiio'ion of the pro{iie of s A. L. Aksent'ev, 26. ptoUlemam Teorii Funkcii Issledovanija po Souremen-ny* Gosvdarstv' Izdat'Fiz-Mat' ttt*tnnogo' 335-340' Kompleksnoro MR23A-52'[4] Lit.. l{oscow,1950'(Rusiian) 2 ? . A k s e n i ' e v , L ' l - ' - O n t n ' u n i v a Vyss' l e n c eZaved' o f t h eIviatematika s o l u t i o n o j(196!)' theinverse Izv' hydromechonics' of problem MR 25-611'[59].' -- ; ^ No.4(23),3-7' (Russran) for star-likeness bounds for coi"'exitycnti 2g. Aleksandrov,i.'n. on SSSR Nauk Akad' and regula' fn a iincte'Dokl' functionsuniuotnni 20-161' [6' 10' 11' l2]' MR go:-90s'(Russian) (N.S.)116(195;t, 2 g .A l e ksa n d ro v,|,.,A.Conditionsfor convexity' the'tnit circlc' univalentinoft|teimageregnn by functio" -zaved. mapping under "g'io'and (1958),No. 6(7),3-6' (Rustrtatematita u.Jun. Izv. V,uss. sian;Mn ?3A-731'[10' 12' 35] 3 0 .A l e ksa n cro v,|.A.onthestar - shopedchor ocler lfthemVyss. appi ngs of o,i' ,ntuotentin thecircle.Izv. a comainbyfunctionsregular MR (tgsg)'No' 4(ll)' 9-15' (Russian) Ucebn.zu"'a' iutematika

on of soyefunctionats definition of Domains A. r. ,,. T;t-T;fL", Issledovaniya rrgulorin a -cir.cle. o7iunctionsunivalent'ond" the class Kompleksnogo Funkcii Teorii po Sou"'ntnnyrn ero!f9111n [6' l0' '12'291 Peremennor;"i'*;tti"n) MR 22A(r)-965' and fi' f'ncti'onsunivalent V/rriationatiroiiemo A' I' Fiz' 32. Aleksandrov, AftuJ' Nauk Armjan' SSRSeT' star-shapedin the circle' rt"' Z--f9'-inutsian'Armenlansummary) Mat. Nauk 14(1961)'No' 4' MR25-426.[6, 1?,29,36] values ^ the functionol "of 33. AleksanO,ou,L' A' Boundary univalent if nobmgryh'(functions J : J(f, f,.f' ,7) on tn"to"q6iel17-3i' (Russian) MR 26-744' in a circle-iiuirst---


SocietetenForhandlingar63(A)' Oeversiktav Finska-Vetenskaps No. 6 (1921).FM 48-403. 16, 17,36, 421 1936' 99i. Nevanlinna,R. EindeutigeAnalytischeFunktionen. Berlin, zbt 14-163. lsgl W. Ed992. Nevanlinna, R. EindeutigeAnalytische Funktionen. J. wards,Ann Arbor, Mich., 1944.MR 6-59' [591 Univ' Press 993. Nevanlinna, R.; et al Analytic Functions. Princeton 1960, 197 PP. Zbl lW-287. l24l of inner 994. Newman, D. J.: Shapiro, H. S. The Taylor coefficients ' functions. Mich. Math. J . 9(1962), 249-255 l59l problem for analytic functions 995. Nishimiya, H. On a coefficient typically.reolinanannulus.KodaiMath.Sem.Rep.9(1957)' 5 9 - 6 6 .M R 2 0 - 1 8 .[ 1 3 , 1 7 ,2 3 ' 5 1 ] the ex996. Nishimiya, H. on the coefficients of functions starlike in terior of a circle.JapanJ. Math. 29(1959),78-82.MR 23A-618. 12, 6 , 9 , 1 7, 2 5 , 3 6 1 Sci. 997. Noshiro, K. on the univalencyof certainpower series.J. Fac. l b | 4 _ 4 0 | .[ 4 , 1 0 ,| 2 , 2 2 , 3 9 '4 3 ] ) ,5 7 _ 1 6. Z H o k k a i d oU n i v . 1 ( 1 9 3 2 1 998. Noshiro, K. on the starshapedmapping by an anolyticfunction. Proc. Imp. Acad. Jap. 8(1932),275-277' Zbl 5-251' [5' 20] Hok999. Noshiro, K. On the theory oJ schtichtfunctions. J. Fac. Sci' kaidoUniv.Jap(1),2(|934_|935)'129-l55.Zb||0_263.[6,1]'49] J' 1000. Noshiro, K. on the univalencyof certain analyticfuncticns' Fac.Sci.HokkaidoUniv.2(1934),89-101'Zbl9-24''12'6'431 Sci. 1001. obrechkoff, N. sur lespolynomes univslents.c. R.. Acad. FM 60-1033'[4, 6, 14'321 Paris 198(1g34),2049-2050. ttal' 1002. obrechkoff, Nr. sri polinomi univalenti. Boll. Un. Mat. l4(1935),245-247.FM 6l-1 154. 132,491 1003. Obrechkoff, N. Sur lespolynomes univalents ou multivalents' ActesCongreslnterbalkanMath.Athenes,(1934),91-94.FM 6 l - l 1 5 4 . 1 4 ,6 , 1 4 ,3 2 i 100.1.Obrechkoff, N. Sur lespolynumes univolentsou m'ultiv1lenls' Bull. Sci. Math. (2) 60, (1935),36-42' FM 62-377' 16' 14' 321 functions- III. J. Nara 1005. ogawa, S. A note on clo,se-to-convex 201 GakygeiUniv. 9(1960),No. 2, 7-23' MR 25-427' 15' 6' l0' Japon Soc. 1006. ogawa, S. on some criteriqfor p-valence.J. Math' . R 2 6 - 6 1 1 .[ 4 , 1 2 , 1 4 , 1 5 ' 6 8 ] 1 3 ( 1 9 6 1 )4, 3 1 - 4 4 1M Univ. 1007. ogawa, s. some criteriafor univalence.J. Nara Gakugei l 0 ( 1 9 6 1 )N, o . I , 7 - 1 2 . M R 2 6 - 1 2 1 0 [' 4 ' 5 l Kodai 1008. oikawa, K. A distortion theorem on schlichtfunctions' Math.Sem.Rep.g(1957),|40.t44.MR19-iol5.[15,24,46,68j

ffi

SCHLICHT FUNCTIONS BIBLIOGRAPHY OF

(PART I)

61

Sci' properties mean muiiivctentfunclions' MR some On .of 169-175' 1009. Ono,l' gun'iLu Daigaku ittt' e' 4(1951)' Rep. Tokvo 33' 431 , ^ - t i in l 3 - 4 5 3 . l g , 1 7, 2 2 , 2 7 " i n tuna t n nrcorono ( t r o t l (cr i r c o l q r e . B o l l . L' S'rie'funzioniunivalenti onoi,i, 1010.

[4] jire40)-' MR3-201' 113-115' Un.Mat'ttiliji

1 0 1 1 ' o n o f r i , L . c o i , , i 4(1942)'21"1-224' o i , o a t t u t e o r i a -MR d e i 7-424' t e T u n[4' z i o19] niunilalerrfi.Bcll. (2) ltal' Mat' zur Un. Theodorsen von desVerfahrens ii'x'on'nrgentz G' z, Math' opit Arch' t012. Gebiete' tthecrv thecryo1 " in variatioiatmethods of Appric-ations . M 125g.Schiffer, Sy*p'rsia irr Applied Math' conformal mappt'i"' i'ot,-"|^tlt ' 8t1956) , g3-113'MR 20-157 l24l in conproblemsand veriationalmethods Ext'eium ' M Schiffer, 1259. formclmapping.Proc.Internat.CongressMatlr.1958,pp. 2||-231'.CambridgeUniv.Press,.N.*York,1960.MR24A-612.

of in thetheory methods $;rlh?i;,?t;lii,icationsof variationot ' 1260. 1958,153pp' MR 20-157tz4l mapptr;.il;araw-Hill, conformal

Mapping cnd D' C ' Lectureson Conformat l26L Schiffer,M'; Spencer' ExtremgtMethods.princetonLectures,|g4g-1950.[59] problew for multiplyC' Tite coe'fficien't 1262.Schiffer, M'; Sptttt"p' 362-402'MR of fvfali''"'2 (2) 11950)' connecteddomainr. Ann.

1 2 -1 7 1 . [5 9 ] d -^* ntrrc /' n vnri ati onol variati on D' C' Some remarks Spencer' M'; of a Schiffer, 1263. ,onn,"ed domains' Proc' mutriply to applicabie methods ,C. S y m p ' 1 9 3 - 1 9 8 ' N u t ' B u r ' o f s t ap n i ' ' A p p l ' M a tMR h ' S e|4-143.|241 r'No'18'

iiqszl. U.S.Govt.Print.ofti.., w",t'., Sur' puicttonati of FiniteRiernsnn C' D' Sptnto' M'; Schiffer, 1264. 16-461't59l 1954'MR faces'Princeton' in ,on,o,iot mayyingof schiichtfunct265.Schild, A. on a problem MR 14-861'[6' .-,o(r953),4-7-51' tions.proc.Amer.Math. soc 1 0 ,1 2 ,1 9 ,3 1 ,3 9 1

FUNCI'IONS (PART I) BIBI-IOGRAPHY OF SCHLICHT

83

Proc' of functionsschtichtin the unit circle' schild,A. Q,r17cluss 1 1266. l 2 o .M R I 5 - 6 9 4 . 1 4 , 6 , 1 2 5' 'l 9 ' A m e r .M a r h .S o c .5 ( 1i S q ) , 1 1 5 321 Proc. claslof univalent,starshapedmappings. a on A, , Schird |267. . , 6 ,l 0 1 1 , 1 5 , l 5 1 - 7 5 7M. R 2 0 - 1 0 4[ 4 A m e r .M a t h .S o c . g ( l g i s, 7 l ' 7 ,2 7 ,2 ) , 31 , 3 2 , 3 6 ,6 3 1 of annuli-Thesrs'Stan, L. The,oniorâl mapping 126g.schmittroitr ford, Univ., 1954't59l | 2 6 g . S c n o l z , D . R , s o n t e m i n i m u275-zg9' m p r o b lIVIII e m s15-802' i n t h e t[59] heoryoffuncJ. Math. 4(195+1, tions.Pacific |2,|0.Schottlaender,s.DerHada.mardscheMultiptikationssatzund weitereKonipositionssatzederFunktionentheorie.Math.Nachr. MR 16-346'l41l l1(1954) , 23.9-294' potenzreihen die im Innern des Einheitskreises r27r. Schur, I. 0a* beschriinktsind.Jour.furreineundangewandteMath., |47(|g|7\,205-232;1a8(1918),122-|4 F M 4' 667(1945)' _475.t59] of5 .Math J' Amer' poiynomials' Fab* On lZiZ. Schur,I. 33-41. MR 6-210.t53l theoremsand criteriaof lZ'73.Schwarz,B. Comptei non-osciltation 80(1955), 159-186.MR Trans.Amer. Math.. Soc. univalence. l7-3',10. [4' 31] , serrcs. of secortdordergeometrrc sutns partiar The . M Schweitzer, r274. D u k e M a t h . J . l 8 ( 1 9 5 : r ) , 5 2 7 _ 5 3 3 . M R 1 3 - 2 3 . t 5 9 ]Amer' functions' theorem for univqlent 1275.Scott,w. T . A coverintg 391 go-g4. 20-877. U9, gsil, MR Math. Monthly 6a(1 |2T6.Scott,w.T.CommentonapaperofC.Utuqay.Proc.Amer. p' 395' MR 2l-662' t19l Math.Soc.10(1959), of clunie'Acta' Fac'Nat' univ' Com1277.seda,v. A noteto Q'p'Qper Russiansummaries)MR enian. 4(1g5g),zss-zoo.(bzech and 23A-56.[5e] bei konfornten Ab1278.Seidel, W. Uber die R'dnderzuordnumg Zbt',1-19' U' z', 3',6', bitdungen.Mat' Ann' L04(193i),182-2131 0 , 2 2 , 3 7, 4 6 ] l of univalentfunctions' Bull' lz.lg. Seidel,W. On the order of growth A m e r . M a t h . S o c ' 4 2 ( l q g 6 ) ' 3 3 5 ' F M 6 2 - 3 ' 7 9 ' 1 6 2 i analytic of functions 12g0.Seidel,w.; walsh, J . L. on the derivstives univarenceand of p-valence. in the unit circreand their radii of Trans.Amer.Math.Soc.s2(|g42),|28_2|6.MR4_2|5.[3,15, 1 8 , 1 9 , 2 2 , 4 2 , 4 1 ,6 2 , 6 B i transform representalz8l. Seshu,S.; Seshu,L. Boinds antl stielties Matn. Analysis and Appl' tionsfor positive,ri functions. _l 3(1961 ), 592-604.MR 25-800' t59l

b--

E4

FUNCTIONS BIBLIOGRAPHY OF SCHLICHT

ond approximation by Generarizedderivatives E. w. g37)' 84-128' zbl Sevrell, r2g2. Soc. tranr. 41(l rnruit,. Amer. polynomials.

O:" r283iffii

sci' Acad'sinica furrctions' thedisto\ti?' :{:'!!"!^t MR 15-948't9l

209-212' Record4(1951)' yunrtions' J' chinese of schriilr't ,oejicients tne on T. rzg4. shah, M R 1 7 - 1 4 1U' 7 ' 3 9 ' 5 4 1 M a t h .S o c '( N ' S ' )l ( 1 9 5 1 ) ' ? 8 - 1 0 7 ' MR l2S5.shah,T.ontheproductofm appin g r a d i3(1953)' i f " r . ? . s yl-7 s t'e m ofnonsi"itu tviattr'" doniairiL--e.iu overlopping 17-141.124,261 luncthe theoryof univalent

1286 n -t+rv,n, 53l 2'vlR k:i;:;,,J{^!iJ"{1{;:\,':roi_' ?,lX? prcductof themopprisradiiof lol.overlappingdo-

t2g7. Shah,T. The il-lo. MR l7-142'l59l Marh.Sinica5(1955), ' Ac' mains.Acta functions ,lroo^ of anatytic i"*, it moi)ii tn, on . T r 2gg.Shah, $g-4s;:tcnin.re. Englishsummarv) ta. Math. sinicastiiisll of convexdomqinsin the p.roperties l*;"')t;ll],rring 421^ffir1,t r28s. e.." Math. Sinica7(|957), *ippi,s. confo,ôi of theorl, ' t9' 241 MR 2J-?89:-10 English 432.(Chinese' "'**u'v) - l,/2 is theradiusof superiority number(3 1290.Shah,T. Goluzin's insubordination.s.i.Recordo'11(1957),2|9-222.MR

oi

tzs| 3ffit: \,

dination' Sci the t1!i\'^:l ::p:::'l?-,' {, i"!r1r tll yg-133' MR 2o-r074'

the Record(N'S') 1(195;jt' of convexcomainsin properties covering some MR rzgz.shah, T. s.i. sinitu 7(1958)'816-828' iipi,ng. confor*rl of theory

ofsubordinainthethecrv '"*' i\'-llotities 3ilt1?i.l'3;11;?X" tzs3

tion.Acta.Math.si,'i.u8(1958),.arl&-+t2,.(Chinese.Engiishsum-

u' 17'l9l ,nuruivrn 2i-1350' tofunction' spaces rineor H. s liitiiirroi, of normed r2g4.Shapiro,

Arbor' theoreticextremalprobtems.l-",cturesonfunctionsofacomplex u"iu. of Mich' Press'Ann pp .lgg-44.'Iire variable,

tzss i?i: t5

t"";?l';':i s' Adn^bounded schticht f uncticn2Zl o ?to', ==r, t19' z(rgse eis-e77.MR 20-1074'

), in Mati. vancement functions.Advancement of schricht coefircients tne on S. 1296.shich, 20-968't17l . sii-e01. (chinese)MR in Math. 3(1957) saddlesurfaces isoprri^riii inequarityfor to ' ce'rrant' the on . M shiffman, F r2g7. and Essayspresented u,ith singularrrirr.-sioai., 9-303't59l irl+al, r;s:-tq+' MR

(PARI' i) BIBLIOGRAPHY OF SCHLICHT FUNCTIONS

E5

l 2 g g . s h l i o n s k y , H . G . o n e x t r e n t q l p r o b l e m s f o r dDokli J f e r Akaci' e n ; i a bNar'rk lefunctionals in the theory iy unfrotint funclicns. (Russian)MR 19-738. 124,601. sssR (N.S.) 113(19s7):280-282. SeeSlionskii' Amei ' mapsof circlesinto con'"exrcgions' l7gg. Shniad,H. on analytic Math-Mon.57(1950)'473-474'MR12-401't10'151 1 3 0 0 . S h n i a d , H . C o n v e x i r y p r o p e r t i e s65'l-666. o f i n t e g rMR a l m15-ll2' e a n s o fi3l analytic paciric J. iurutrt.ltr953), functions. potenzreihen;nit monotoner Koef-fizientenfolge' r301. sieron,S. ilbe, A c t a L i t t . S c i . S z e g e d g ( 1 9 4 0 ) , 2 4 4 - 2 4 6 . M R | - 2 ; 3 . [ 4dans , ? 2 ,le 39| lesfonctions univalentes,atg^briques sur L. Siewierski, 1302. demi-plan.Bull.Soc.Sci.Lett.Lodz.Cl.IiIMath.}iatur. 57] 7(1956),No' 4' l7 p ' Zbl 90-291'[9' l303.Siewielski,L.surlavgriqtionlocaledesfonctionsunivglentes, a l g e b r i q u e s d a n s l e d e m i - p l a n . B u | l . S o c . S c i . L e t t .57] Lodz.Cl.III g(lg5Zi, No. 3, 16 p. zblgo-291. [9' Natur. Math. Sci. extre,rtalesdans /esfamilles des 1304. Siewierski, L. sur resfonctions dons le demi-plan' Bull Soc' fonctions univalrnrrr,'o4AOrfques Natur. 8(1957),30 p ' zbl90Sci. Lert.Lodz. cl. rir sii. Math. ? 9 2 .[ 9 , 5 7 ] (Jnivalentand multivolentfunctions' Math' Student 1305. Singh,'S.Ii . 30(1962) ,79-90. MR 26-743' t44l 1 3 0 6 . S i n g h , S . K . ; S h a h , s . M . o n t h e m o x i m u m f u n c tl2l-128' i o n o f a MR 22(1954)' meromorphic function Math. Student 16-459.[9' 16] l30T.Singh,Y.Interiorvariationssndsomeextremalproblemsforcertainclassescfunivalentfunctions.PacificJ.Math.T(1957)' 1485-1504.MR 20-20' 122'241 problems for o new classof univalent 1308. Singh, V. Some extremil 7(1948),gtt-gzt. I\{R 20-771'u5,17 ' .frnctions.J. Math. Mech. 241 coefficients' of the bound1309. Singh,Y. Extremumproblemrf?'the edunivalentfunctions.Proc.LondonMath.Soc.(3)9(1959)' 24',?0',391 3g7-416.MR 22A(l)-18' t17'22' and coefficients of bounded I 3 10. Singh, V . Grunsky inefuatities Fenn' AI No' 310(1962)'22 schlichtfunctions. Ann. Acad. Sci' ' 14,221 PP. MR 26-2'77 ,c.^^^-h,,tn Uspehi conformal mapping of nearby-regions' onv . 1311.Siryk, G. l)' 57-60' (Russian)MR 19Mat. Nauk (N'S') 11(1956)'No' 5(7

2s8.[5el univalentfunctions' 1312.Stiottttii, G. on finite sumsof bounded -709 MR 15-516' 707 , Dokl. Akad. Nauk SSSR(N'S') 93(1953)

b*--

86

BIBLTOGRAPHYOF SCHLICHT FUNCTIONS

u 6 , 2 0 , 2 24 , 31

univalent functions'Dokl' 1313.Slionskii,G. on thetheoryof bounded MR 18(Russian) Akad. Nauk SSSR(N.S.i ril(1956), 962-964' 7 9 8 [. 9 , 15 , , 2 2 , 5 86, U problemsfor differentiablefunc1314.Sii""rtii, G. on the extremal vestnik Leningrad' tionslsin the theoryof univalintfunctions. MR Englishsummary) No. li, o+-s:. (Russian. Univ. 13(1g5g), 20-77r. t24l schtichtfunctions.vestnik r 3r 5. il";rl;i, G. on thetheoryof boundeti (Russian' EnglishsumUniv. l4(1959i,No. t 3,42-51' Leningrad 't221 nrarY)MR 22A(l)-455 L. N ' On a problemof-thetheorYof univalentfunc1316.Slobodeckii, 235-238. MR t;o;ts.Dokt. Akad' Nauk SSSR(N'S') 92(1953), 1 5 - 4 1 3t .9 , 1 5 ,5 8 ,6 0 1 desfonctions univalentes' r3r7 s;;"k',-L: contribution i la theorie CasopisPest.Mat'e2lg32)'l?-19'Zbl6-&'14'6'10'17'36'38' 421 for the argumentof an analytic G. S. on someestimates E*0, 1318. function.Dokl.Akad.NaukSSSR(N.S.)92(1953),7||-7t3. MR 15-613't59l (Russian) ihrorr* in functiontheo'';''Izv' Vyss' 1319.Spak,G. S.,4 coverin'g 218-223'(Russian) . Za,,ed.Matemulitu(1959),No' 1(8), Ucerrn MR 23A-731.[l , 19,221 aprv s1 Jor the modurusand rear r3zo'$0"[-o. s. some estimates pseudo-positivefunctions.Izv.Vyss.Ucebn.Zaved.Mat.|9o2, -lzo.6(31), 148-154' 12,15' 561 |32|.Specht,.E.J.Estimgtesofthemappingfu nctiongndits nearly circular regions' derivativesin conformal mapping of ' t59l MP' 13'337 Trans.Amer.N{ath.Soc.7l(1951),183-196' valentfunctions' II' Trans' 1322.Spencer,D. c. on finiteiy meon 2-82 13,17,33i Amer.lviaih.Soc.+girg4oi,418-435.MR ' i ' Lonidentities , D. c. I'roteon ,o*,, fun'ction-theoretic 1323.Spencef 2-82' 13' 271 a -don Math. Soc'15(i940)'84-86'MR Proc' Nat' Acad' Grunsky' o-f inequatity an on c. D. 1324.Spencer. 616-621'MR 2-79' U8' 191 Sci.U.S.A. 26(1940), valentfunctions'Proc' London 1325.spencer,D . c. on finitely mean 16, l'.i' 18'3],45' Niath.Soc.Q) 41(tg+z),iot-LlLlvIR 3-79.[3,

s2l in onalytic transformations' J ' 1326. SPen;cr, D. C. On distortion g4l), 124-126'MR 2-186' U6' Math. PhYs.N1ass.Inst. Tech. 20(l 1 9 ,3 3 1

FUNCTIONS (PART I) BIBLIOGRAPI{Y OF SCHLICHT

87

of Math. (2) one.valentf;;ictions. Ann. mean on C. . D |377. Spencet, 16' 17' 19',27', 331 42(lg4l), 614-633'MR 3-78' tl5', iS2S.Spencer,D.C.Note.onmeanone-vqlentfunctions.J.Math. Fhys.Mass.Inst.Tecrr.2l1lg4z),i78_188.MR4-138.[331 |32g.Spencer,D.C.Someremarksconcerningthecoefficientsof schlichtfunctions.J.Math.Phys.Mass.tn't.Tech.,2I(|942),

54i 63-68.,rnn4-76.t16, l7 , 42',

identity.Amer. J. Math' A function-theoretic c. D. Spencer, 1330. 461 ' , t47-160'MR 4-137 [33' 55(1943; ionfornrut mappins' Buti' i! problem, Somi C. . D Spencer, . I 3 I3 417-!39'MR 8-515'l4/'l Amer. Math' Soc'Sltrq+T' mappingsof the problem1or schlich-t t332. Springer, G. The,orlitfrni e x t e r i o r o f t h e u n i t " c i r c l e . T r a n s . A * . ' . M 5a3t h' 5 .Soc.70(1951)' 1 6' , 1 7 ' , 2 4 ' 2 5 ' , 2 7 ' , 8 1 t 5 ' 1 3 2 4 ' t n ' M R 421-450. FunkHi)ueschrichter derkonvexen Extreme'p'unkte G. Springer, 1333. t9', 15',17', i{R 16-1011' 230-232. fionenMath.Ann. t)g0955),

u:t1:*"!:::KX'ri:i'-'::; "#;o;{ , . onthemean 1334.3?;"1-l;,i'i'*. derivatives,Riv.Mat.Univ.parmaS(1957),361-369.MR21_ 1 0 6 3 .I 5 9 l .^rAr rRiesz' J' Loncl o n M a t h . S o c . P ' On a theorem o'f M' Stein, 1335. 8 ( 1 9 3 3, 2 ) 4 2 - 2 4 7 'F M 5 9 - 3 2 5 '[ 3 1 Proc' methids in conformsl mapping' 1336. Stone,M. H . Hitbert-rpo,, pp' 409-425' spr.., (Jerusalem1960), r-in!u, Sympor. Internat. JerusalemAcademicPress,Jerusalem;Pergamon,oxford;1961.

MR 25-39.t59l

andunivalent betweentypicary-rear 1337.Streric,s. I . on a connection(N.S.l nig57) No' 3(75)pp' 2llNauk functions.uspehilurut. 13' 4U ' 220.(Russianirurn 19-643'[4' an.alvticin o ctrc:k. functions 133g.Strelicas,S. Someîrop,irr,:;{ Daiuai. Mat' Fiz' chem' Mokslu vilniaus valst. univ. Moksl0 MR 22A(2)summary) Russian (Lithuanian. 6,7_71. Ser.4(1955), 2 0 9 3 . [3 , 4 , 1 7, 541

. ?,'(z) ,-, ..sl n* der Frerl i nhuns d, dA SS unter ,tor Bedinbung Ar.cf 1339.Stroganoff,w. G . \be, den f(z)diekonformeAbbildungerne,st.ernartigenGebietesaufdas Mat' Inst' z-Ebene tiefert' Trudy innere des Einheitskreisesder S t e k l o v a 5 ( 1 9 3 4 ) ' z ' + l - Z S g ' Z b l 9 - 1 7 3schlichten ' [ 6 ' 1 5 ' 6 8Funktionen' ] Th-eorieder 1340. Strohhhcker,E. B'eitros,,u' Math.Z.37(|933),356-380.nbl7-2:I4.|2,6,10,15,17,|9,29,

u3'u?rll|"r*, Einfachzussmmenhangender Abbitdung 1341i?;jr?;

E8

BIBLIOGRAPHY OF SCHLICHT

FUNCTIONS

Bereiche.B.C.Teubner,LeipzigandBerlin,lgl3.FMM_755.||, 1 0 ,3 7 1 |342.Suetin,P.K.Faberpolynomials-forregionswithnon-anolytic boundaries.Dokr.nr l.Norskevid. Selsk.Forh.Trondheim [9, 17,251 168.MR 2A-6(A'. ein kceffizientenProblemfilr schlichteAb\bq . l4sz. Waadeland,H bilCungendeslf l I'{R 20-664'[9, 17' 251 168-170. 30(1957), von scott' Bedeckungssatz 1453.waadeiand,H. Bemerkungzu einem 112-116'MR Norske vid. Selsk.Fcrh. trondheim 32(1959), 24A-370.U7, 541. ncr' (Jntersuchungen uber Aquivalenzklassen 1454.waadeland, H. Tron' Skr selsk' mierter, schtichterFunktionen Norske vid' 541 24A-254'Il7 '29' dheimirqsgl,No..3,47pp' MR I, II' Funktionen. 1455.waadeland,H. uber biichrankteschlichte MR Norskevid. selsk.Forh.Trondheim32(1959),84-91'92-94' 2 4 A - 2 5 4U. 7, 2 2 , 2 4 , 3 0 1 Funktionen.Nor1456.s'aadeland,H. zur The'orieder beschriinkten MR 26-748' 82-85. skevid. selsk.Forh. Trondheim35(1962), 115,22, 6ll

.

, r

a :^ - - ^ r \ T ^ . . V . ^-L

Fractions' New Yo:k' 1457.Wall, H. S . Anaiytic Theory of Continued Van Nostrand, 1948' MR 10-32' t59l curvesof Green's 1458.Walsh, J. L. Lernminscatesand equipotential function.Amer.Math.Month|ya20935),|_|7.t59] l 4 5 g . W a l s h , J . L . N o t e o n t h e c u r v a t u r e o f t e v e l c u r v e s o f G r e FM en's Sci. u.s.A' 23(1937),84-89' Acad. Nat. Proc. furtctictn 63-297. [9' 10] of Green'sfunctions' 1460. Walsh, j. l-. On the shape of level cttrves g37),2a2*213.FM 6-7-296.t59] Amer. Math. Monthrv ++(r traiectoriesof 1461. Walsh, J. L . Noteon the curvatureo.f orthogonal Amer ' Math ' Soc' level curves of Green's functions . Bull ' 44(1938) , 520-523-Zbl 19-271' [59] 1462.Walsh,J.L.onthecirclesofcurvatureoftheimagesofcircles a6(1939)'472-485' undr a conformal map. Amer. Math' Monthly M R 1 - 1 1 1 .[ 1 9 ' 3 5 ] analytic in the 1463. Walsh, J. L. Noteon the derivotivesof functions 515-523'MR 9-23' unit circle. Bull. Amer. Marh. Soc. 53(1947),

u 5 , 1 7 ,1 8 ,1 9 1

96


mapping of multiply connected 1464.Walsh, J. L. On the conformal 128-146'MR l8-290' regions.Trans.Amer. vrattr.Scc.82(i956),

t60l | 4 6 5 . W a l s h , J . L . I n t e r p o l a t i o n o n d a p p r o x i m a t i ocolloq' n b y r a Publ'20' tionalfunc Soc' in the complexdomain Amer' Math' tictns

t5el 2ndEd. (1e56)' mapsof multiplyH. J. on canonical Landau, walsh, J. L.; 1466. 81-96' Zbl Trans.Amer. Math' soc' 93(1959)' connectedregiorzs. 86-281.

[59]

.. , , , , - , ) ^ - , r ' x t n t t t , n o ,der A lrder Abreitungl o r Ab' Randverharten das Uber s. warschawski, r46i. Z' 35(1932)' bei koiformer Abbildung' Math' bitdunssfunktion 321-456.Zbl 4-404.u9' 461 at theboundaryin conderivatives 146g.warschawski,s. on int'nisier 310-340'Zbl Trans.eler. Math.Soc.38(1935), formatmapping. 14-267. t59l . ? - . , ^ - - ^ ^ L t i n h r , > r Funk .. , ,, schlichter F r t n k . warschawski, S. Uber die winketderivierten 1469 t i o n e n . C o m p o s i t i o M a t h . 4 ( 1 g 3 7 ) , 3 4 6 _ 3 6 6 . 2 b | | 6mapping -407.t46] method of conformal 1470.warschawski, s. on Theodorsen's o-fnearlycircularregions.Quart.ofApplieciMath.3(1945), 12-28. MR 6-207. t59l regions' s. on conformal mappingof nearly-circular warschawski, l4TL P r c c . A m e r . M a t h . s o c . l ( 1 9 5 0 ) , 5 6 2 - 5 7 4 . M R 1 2 _in 170.[3] of the boundory confor' on-diffe'rentrabttity s. warschawski, r4iz. molmappmg.Proc.Amer.Math.-Soc.|2(|961),614_620.MR

24L-2s3.t59l

DaJ@d' DukeMath' J' series 1473.whittaker,J. M. A noteon the 2l(rg54),571-573'MR t6-232' t59l pour la classedefoncde-Koebe 1474.wiatrowski,P . sur i tn\orbme 10(1959)' bornees.Bull' Soc' Sci' LettresL6d'2 tionsunivalentes

Ne. 14, 13 pp. MR 24A-37' t19] ^ r ,, .- --^)it- Enttr' variation of a function and its Fourrer 14j5. Wiener, N . The quudratic c o e - f f i c i e r r f . s . M a s s . J . M a t h . 3 ( 1 g 2 1 ) , , 7 2 _ 7 4the .FM 50_21i3.[591 quantum from 1476.wigner, E. P. on a classof enalyticfu'ictions (2) 53(1951)'35-6'7' I''{R theory of cottisions.enn. of lvlath'

mapsof convex sequences f9y ordinating factor *rllt;l?.t3],, r4.ti ), 689-593' MR so.. 12(196i

the unit circle.prol. em.i. Math. 2 3 A - 4 1 51. 1 , 2 ,1 0 ,1 6 ,4 i i of certoinentirefunctions' llr47g.wilf . H. s. Therartiusof inivarence l i n o i s J . M a t h . 6 ( 1 9 6 2 ) , 2 4 2 _ 2 4 . } , I P . 2 5 -schiicht 426.t28] of funcfions, coefficients the of Averages ivl. G. Wing, A7g.

FUNCTIONS (PART I) BIBLIOGRAPHY OF SCHLICHT

91

iroc.Amer.Math.Soc.2(|951),658-661MR13-123.||7,20,42, 541 l4S0.Wintner,A.onthe.principleofsubordinationinthetheoryo'f gnal},iicaifferentialequat.ions.ActaMath.96(1955),|43_156.

Studia Funktionen' rheoriederschtichten , $l,i,l;;it*ltirgj r48r ::, i0' l5' 58' 5+] 4(1933t , 66-69'Zbl8-319'[9' N1ath.

ru, t4?lyltr6sse einesschlitz-sebietes' nemelrlsH. wittich,' t4g2. rbr-:05' MR r2-49r' t49l Arch. Math. 2(195C)' Gebiete'Math' k!!i;;men ,Abbiirlungschllchter zur . H wittich, 14g3. MR 20-.401'U9' 241 Nachr. l8(1958)' 226-234' Ann. Acad' Abb,dung schticiterGebiete. Koiforye H. r4g4.wittich, (tvis), 12pp'.I\iR'20-53,'t49l sci. Fenn.ser.A. I. No.249i6 et d partierbette tlotomorphe ;';-t6grate-qLi:'f"::'::i r485.wolff ,";" p o s i t i v e d a n s u n d e m i p l a n e s t u n i .'vt'2' o l e41 nte.C.R.Acad.desSci. ' Zbl8-363 (Paris)lg8tfq:+)' l2O9'-1210 c' R' Acad' u-niluarentes' horomorphes 14g6.wolff , J. sur resfonctions M R 5 - 3 6 ' l ' 2 24' 9 ' 6 2 1 S c i .P a r i s2 1 3 ( 1 9 4 11)5' 8 - 1 6 0 ' Nederl' ,i*it^ po, kslonctiin.sunivalenles' ' MR p' 163 1 t4g.twolff , J. In6gqlit6s Errata prloir-. U, bSO-6el (19a1); Akad.Wetens.h.,

d'unefonctionhotodurradiriv'ee i;'.,li, ,"r'.t];31',il'"ru*es de la 1488 dansun demi-planau voisinage et iorn6, morpheunivalente MR P,o.. +str942),574-5,77. Wetensct,., ntaa. Nederr. frontibre.

3:" I48e. i;3ift,"1." nugatit6s,'i * p:: i ^:::..'':, : :':::';, l: :r,{",:'

h o l o m o r p h e s , u n t v q l e n t e s e t b o r n ,MR e e s5-231' d q n s u 122' n d e 571 n.i-plan.Com-

ment.Math'Helv' iiirq+'' ?9--6.2g8' analytique des W. Su, i^ cotefficients fonctions

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_

-.!

98


u , 6 , 1 0 ,I 5 , 2 3 ,4 9 ,6 3 ,6 4 1

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4el

die p-wertigen Funkl4gg. Yosida, Tokurrosuke Bemerkungen i)ber gM),16-19' MR 7-288' [9' tionen Proc. Imp. Acad. Tckyo 20(1 1 4 , 1 5 , 1 7 , 2 5 , 4 3 '5 8 1 p-wertigen Funktionen' 1500. Yosida, Tokunosuke Ein Satz uber die Proc.Imp.Acad.Tokyozo(|g4p;),409.MR7-288.[14'15] on the boundaryvaluesof 1501. Yurchenko,A. K.; Durldudenko,L. E. in the circle lzl functions regular and univalent ukrain. Mat. z. 9(1957), 455-460'(Ruscertain spec;al classes.

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hr----

100


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260

B IBL IOGR AP H YOF S C H LIC H T FU N C TION S

1020,t021,1023,t024,1025,t026, I104, 1124,1126,tt62,r164, , 301, 1201,1203,1205,1206,1 2 1 2 ,1 2 1 6 ,l2l7 , 1243,1262,t 2 9 2 1 1 3 3 3 , 1 3 31347, 5 , 1348,1 3 7 6 ,1 3 8 4 ,1 3 8 6 ,1 4 0 2 1, 4 1 1 ,t413,1429, l48g 1469 1482, , 1492,1497,1498,1 5 2 7 , 1 5 3 9 1 , T20. Partial Sums(Cesiro sums). [3, 125,139,r47, 193,2m, 2M, 436,442,+47, 448,451,452,540, , 087, 6 3 5 ,6 8 7 , 6 9 06, 9 1 ,7 2 0 , 7 4 6 , 7 5 3 , 8 3 6 , 9 1 0 , 9 1130,6 0 ,1 0 7 6 1 15291 1487 1352, 1323, 125A, n2l, 1222,1,244,1249, , T2l. Coefficient Bounds (relations) -fo, Functions (functionats) of Positwe Real Part of Topic 2 . [15, 107,125,139,147,2M, 436,450,459,462,540,542,571,585, 5 8 8 ,6 2 7 ,6 2 8 ,6 2 9 , 6 3 5 ,6 4 0 ,6 4 2 ,6 5 7 , 7 4 68, 2 4 ,8 6 9 ,8 8 3 ,8 8 5 ,8 8 7 , 9 0 7 , 9 1 0 , 9 1 3 , 1 0 8 6 ,1 0 8 7 ,I 1 8 7 , 1 2 2 2 ,1 2 4 9 ,1 2 5 0 ,1 2 5 6 ,1 2 8 1 , 1323,1352,1415,1467,15i31 T22. BoundedFunctions (functionals). 1 4 , 3 1 , 3 25 , 9 , 9 1 .I I ! , I 1 5 , 1 2 5 ,1 2 7 ,1 3 0 ,1 5 4 ,1 5 6 ,1 6 6 ,1 7 0 ,1 7 9 , 180, 2 \3 , 236, 237, 238, 265, 216 ,28 I , 295, 297, 305, 306, 307, 30E, 3 0 9 ,3 2 3 , 3 4 1 , 3 5 13,5 3 ,3 5 3 ,3 8 4 ,3 8 5 ,3 8 8 ,4 1 8 .4 3 0 ,4 3 1 , 4 3 2 , 4 3 3 , 134,438,450,453,496,497,507,522,536,588,605,621,622,624, 625,626,661,693,704,732,733,i34, 798,800,801,846,854,856, 883, 891, 895, 904, 919, 927, 936, 937,938, 962, 963, 971, 1050, 1 0 5 2 ,1 0 7 8, 1 0 9 2 ,I 1 2 8 ,1 1 5 5 ,I 1 6 3 , I 1 6 5, 1 1 7 3 ,1 1 8 7 ,1 2 0 1 ,1 2 0 3 , 1205,1209,1210,l2ll, 1229,1233,1242,1249,1251,t253, 1262, 1264,1271,\272, 1275,1276,1277,1290,1296,1298,1306, l40l, 1329,1347, 1354,1356,1357, 1367,1368,1369,1375,1381,"328, 1402,1418,1422,1423,1424,t425, 1426,1427,1443,1473,1477, 1 5 1 6 ,1 5 2 8 ,1 5 1 2 i, 5 6 0 1 T23. RepresentationTheorems(formulas). [ 4 1 , 1 3 0 l, 5 l , 1 7 8 ,1 8 4 .1 8 7 ,l 9 l , 1 9 2 , 2 7 3 , 2 7 82 ,8 8 ,2 9 3 , 3 \ 9 , 3 2 5 , 3 4 0 ,3 4 7 ,3 5 2 , 3 5 53, 8 2 ,4 0 9 ,M 5 , 4 6 5 ,4 6 9 , 4 8 14, 8 3 ,5 1 3 ,. 5 1 65, 4 2 , 5 4 6 , 5 5 15, 8 1 ,5 8 3 ,5 8 5 ,6 6 0 ,6 8 1 ,7 0 7 , 7 7 9 , 8 0 28,0 8 ,8 1 9 ,8 7 2 ,8 7 3 , 874, 879, 892, l0l I , 1012,1014, 1034, 1035, 1039,lM0, 1043, 1 0 8 0 ,1 0 8 3 ,1 0 8 8 ,11 0 5 ,11 0 6 ,l l 1 3 , 111 8 , l l 1 9 , 1 1 2 0 ,1 1 2 3 ,1 1 2 4 , 1125,I 138,I 153, 1207,1234,1256,1273,1327,1335,1342,134?, 1 3 4 8 ,1 3 8 2 ,1 3 8 5 ,1 3 8 6 ,1 3 6 7 ,1 3 9 7 l, 4 S , l 4 0 l , 1 4 1 9 , 1 4 9 11, 5 0 2 , 1 5 1 0 ,l 5 l I , 1 5 2 0 ,1 5 2 7 ,1 5 4 0 ,1 5 4 8, 1 5 5 4 ,1 5 6 0 1

TOPIC REFERENCES

261

Methods' T?A. Variationai(symmetrization) 55' 56',68',82',83',84',87',89',90', [18,19, 37,42,44,45,46,52,53, i i l . l ! 5 , 1 3 1 , 1 3 3 , 1 3 1 , 1 5 2 , 1 6 7 ' 1 6 8 ' 1 6 9 ' 1 8 4395', ' l ? l ' 2 3 042r', ',235'238' 391',392', 408', 3n:,313'341'342', 250,251,287,288,3U6; 498',500',530',532',569',576', 422,474,425,426,$2:, 434,485'486' 645 648', 651',661', 662',672' 601,601 , 612,626,633;$6:,638' 642:', ', 49,7 52,758, 7 60,769,792,808' 74|, 7 42,,.1 676, 7 03,7 07,7 33,7 34,, 896', 895', 860;875'!78',890',892',!?3'894', 842,843; 813,831,833, gl 98r', 938'gll'95i', g54' >' 976',982', 891,gl4, g20,g23,934"935: l 1 0 5 5 1, 0 5 8i,1 0 5 ,1 t 0 7 , l 0 E , 9 8 5 ,1 0 0 71, 0 i 2 ,1 0 1 3 |, 0, 2 5 , r c i a e . | | | 2 , 1 1 1 3 , 1 1 1 5 , 1 1 2 0 , t | 2 | , | | 2 2 , 1 | 2 3 , 1 112c6', 3 0 , 1!1209 3 1' ,1212', 1138,||,46, 1205 ' 1201' 1l?5' fi73' 1170; 161, i 1150,1152, 1225,1256,1266,1269,1271'1273'1274',1276',1341',13M'1383' 1432,1472,1478,15021 univalentFunc' Bounds(relations)for Meromorphic T25. coefficient 'toPic 9 ' tions of U 7 6 , 2 6 5 , 2 9 6 , 3 1 4 ' 3 1 5 ' 3 1 6 ' 3 3 18'8333g ' 5' C t 64' 3 51'8038' 6014' 174' 616' 4 ' 6 8 8 ' ,1 0 '3, M 7 0 8 ,7 1 2 , 7 4 9 , 7 5l0i t,, 7 6 4 ' 7 7 1 '8 4 3 ' , l4/ts',t 146',15221 1170,1171, 1234,l27g:,n3;',2'l4lg', (imagedomainshaveno common T26. (Jnrelated(di.sioint)Functions values). u5,59,60,88,89,90,196'308'512'514',515'6/'6',651',73t',811', 8I 6, 1019, i 42ll T27, Are,l Principle(and generalizations). 1 g , 6 2 , 2 6 5 , 2 8 2g, 2 , ',589',611' '5, 01250' 1,' 5135431' 3- 5688' 134' ,2538' 7 i +9, 6 , 3 3 8 ' 4 8 1 ' 591416'1 6 4 7 , 6 5 6 , 8 1 0 , 8 l l , a i o ' 8 2 3 '8 4 5 ' , 1480,15241 (suchas Besselfunctions'or of Functions speciat of univalence T28. functionshavingsPecialforms)' I24,25,121,322,469,675'700'701',?88',989'1016',1300',1M7' 1457.1458,14661 T29. RegionofVariabitity(ofcoefficients,orofcertainfunctionals). g2,1g7,237,238',240',242' 146,47,48, 49, 54, 6 8 , 1 6 0 , i ' 7 1 , i g \ , 1470, 47| ,485' 525', 528', 623', 467, 465 , 42g ,430, 2M,314,319,373,

262


6 3 6 ,6 3 7, 6 3 8 ,6 4 7, 6 6 1 ,6 8 3 ,7 2 5 , 7 3 3 , 7 3 4 , 7 4 1 , 7 4 9, 873787,8 4 2 , 1105, lcp.z,1024,1026,1049,1058, 886,921,936,937,946,982, 1 2 0 8 ,1209, l z 0 / , 1 1 1 4I,l 1 6 , I 1 3 0 ,I 1 4 8 ,1 1 7 3 , 1 1 7 14 1, 9 7 , 1 2 0 2 , 1210,l2ll, 1250,1259,13M, 1350,1355,1370,1371,1379,1382, 1 3 9 41, 4 7 8l,5 l l , 1 51 7 ,1 5 2 11, 5 4 81, 5 4 9 1 T30. Coefficient Bounds (relations)for Bounded Functions of Topic 22. 1127,170,180,281, 305, 306, 309, 358, 431,450, 536,588,624, 5 2 5 , 6 9 3 , 7 3 2 , 8 0 0 ,8 0 1 , 9 0 4 , 9 2 7 , 9 7 1 , 1 0 9 2 ,1 1 5 5 ,! 1 8 7 , 1 2 5 1 , 1271,1272,1275.1276,1277,1306,1328,1329,1368,1402,1418, 1422,1423, 1124,1425,1426,1.532! T3l. SchworzianDerivative, the Differential Equation w" * Qw 0. [8, I 3, 72, 78, I 35,227, 228,2o5,268,274, 334,337,370, 407,495, , 9 7, 9 8 4 , 9 8 7, 1 0 1 4 ,1 0 1 9 , 5 1 2 , 5 5 5 6, 9 6 , 7 6 2 , 7 7 38, \ 1, 8 2 3 , 8 5 8 8 105C,1052,1063,1090,1221,1304,1486,1494,15431 T32. Univalenceof Polynomlals(Schild, Remak, Hurwitz). u 2 2 , l z ' J , 1 2 4 ,1 7 l , 1 7 4 , 2 4 9 , 2 9 4 , 3 7 2 , 4 3 5 , 4 7 31,8 4 , 5 8 0 ,5 8 4 , 593, 659,746,799,830,910,919,929,932,1062,1091,I I 17, l'^45' 1183,1185,1186,1187, 1236,1237,1238,1239,:241, 1242,1252, 1 2 8 5 ,1 3 1 7 ,1 3 3 5 ,1 3 6 6 ,1 4 0 3 ,1 4 0 6 ,1 4 0 8 ,l n 9 , l 4 2 l l T33. Mean-valentFunctions (and generalizations). 86 , 2 , 3 6 4 , 3 6 65, 5 8 ,5 6 0 ,5 6 1 ,5 6 2 , n, 6, 7, 132,210,212,282,353 9 7 6 , 9 7 8 , l M z , 1 0 4 4 , 1 0 4, 5l M 6 , 8 8 0 , 8 8 1 , 6 5 4 , 8 7 8 , 6 5 3 , 5 6 3 ,5 6 5 , 1 0 4 7 ,1 0 5 1 ,11 5 3 ,11 5 5 ,1 3 0 3 ,1 3 0 4 ,1 3 7 6 1 T34 Bieberbach-Ei!enbergFunctions (generalizations and related classes;Grrelferfunctions;Aharonov pairs, etc.) 5 ,0 q ,5 i l , 5 1 2 , 5 1 56, 0 5 , 6 0 8 ' [ 9 , 1 1 ,i 5 , 1 8 ,8 8 , 1 3 8 , 2 6 2 . 3 0 7 , 3 0 8 646,651,1020,1021,11,J0,14931

T35. Curvsiure.LevelCurves. u 8 , 5 4 , 6 5 , 2 3 53, 5 0 ,3 7 4 , 3 7 5 , 3 7 83,8 0 ,3 9 8 ,4 1 2 ,4 7 3 ,4 7 4 , 5 0 E ' 620,659,682,895,9I 8, 921,957,972,973, 991, 520,525,528,539, 8372, ,1 1 0 4 1I,1 0 6 ,l l 2 7 , l 1 3 5 ,I 1 4 3, i 1 4 4 ,1 2 7 31, 2 8 61, 2 8 7 , 1 2 8 1551,lst9rl 1 3 9 J1, 3 9 5 , "171,

.d

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263

of ropic 6' (reretions) for startikeFunctions T36. coefficientBounds 602 [ 7 0 , 1 0 1 , 1 1 8 , 1 2 6 , 1 qSg, 6 3 , 488. 1 7 0 S1S ' 1 7 6S+0,, ' ! 7 g553 ' 1 8 8 ' l 9587 l ' 1'9601 2 ' 2' 5 3 '', 2 8 1 ' 3 4 3 ' , , 4SS :58!; ,458, 347 ,348, 345 , 6 2 9 , 6 5 8 , 5 8 8 , 6 9 3 , 7 1 2 , 7 7 6 , 8 5 2 ' 8|5277'3, 8,18370' 181,8381' ,9?1,M 3 3' ,01,c r O 9 ' , 1 0 8 7 ' 1 1 7,1| 2 4 8 , | | 2 2 , | | 3 2 , 1 1 3,3 | i 1 q , l 1 7 0 , 1418, 1 3 8 7t'+ o z , l 4 1 51, 4 1 6|,4 | 7 , 1 3 3 11, 3 3 51, 3 4 8|,3 4 g , 1 3 5 6 , ' i5431 1467,1510,151I, 1522'1527 Lemma(andgeneralizations)' T37. schwarz's 1186'12541 [388,482,1085, convexFunctionsof TopicI0' (relations) for Bounds T38. coefficient t 1 4 3 , 1 4 4 , 1 4 5 , 2 8 1 , 3 4 6 ' 61470', 9 3 ' 714911 12',867',904',1122'1220'1248' , l4l7' 1418' 1273,1319,1335 (suchas gaps'realness'rnonocoefficients on conditions special T39. tonicitY,etc')' 244'248'364' 237 201,214,236, 150, 53, :2?|'240;2!):24,2' U2, 558'624',625', &g,+ro' +g5'489',46',4gl',4g2'5-42' 834',85I' 373,376,395, 805', 7 84',790', 'llg7 7'91', 7 33,7 34,7 47"7 5l' 7 52',7 83'', 663,684, ' 12'71'12'78' ', 1265 ttry',--tigz' g37 irss ' ,1056, 908, 886, 1305,1313,1314,1118'1335'i359'1439',1478',15251 T40.FunctionswhichareStartikeinoneDirection. ' 13011 1524,642,853,1297 in OneDi;ection' T41. Functionswhichore Convex 8 3 4 '8 5 3 ' , 8 ' , - u L7' ,4 7 ' , 5 4 2 '5 7 1 ' ^ l ? ' , 5 7 56' 2 5 2 4 ' 5 1 3 , 3 N , u13, l2g7' 1301'14191 1235', ,121;'1zzo' 1223' 926,1203,1205 (la" I s n)' Coniecture T42.Bieberbach u 2 , 1 4 , 4 5 , 8 7 , 1 6 7 ' 1 6 8 '424',' 1 8 7 'qis', 3 3 3q2s',485', ' 3 3 6 ' , 35310', 9 ' 550', , - 3 3593', 9 ' , 3594' 40',359',360', 423' 422' 421' 408, 405, 395, 1068' 1067' 1065', gzl' lnz0',1064', 610, 649,655,724'-767'9M', 1200, l ,d i , | 0 g 7 ,1 0 9 81- ,1 0 01, 1 0 1 , | 0 1 4 , 1 0 7 5 1 0 7 3 , 1 0 7 0 , 1069, 1483' t265"1304;1315' 1325'lM' rzrg, tzzl, tz26,1zsoi,l24g' 15081

2M


T43. Radiusof Univalency(p-valency)(of various classesof functions). ',206, 2r2, [30, 3 l, 32, 54, 103, 116, 119, 122, 142, 146,178,205, 437, 438, 436, 428, l, 39 340, 214,224,228,253,256,257,288, 293, ,720448,449,454,460,475,478,482,522,5M, 572,699,702,707 1 0 7 8 ,1 0 8 1 , l 0 ' t 7 , 1 0 7 6 , 1 0 5 2 , 1 0 5 0 , 7 4 6 , 7 5 3 , 8 2 88, 8 2 , 9 1 0 ,1 0 1 6 , 1087,1088, 1094,1163,1189,1198,1227, 1241,1242,1244,1249, 1 2 6 41 , 2 9 8 1, 3 0 4 ,1 3 0 5 ,1 3 0 7 ,1 3 1 4 ,1 3 1 7 , 1 3 1 81,3 8 1 ,1 3 8 8 , l M 7 , 1448,1M9,1450,1451,1452,L453,1454,1455, 1456,1457,1459, 1460,l16i, \462,1453,1485,1503, 1528,L529,1555] T/g. SurveyArticles, Books, Cotlections of Various Papers, Symposiums, BibliograPhies. 371, 1 2 2 , 3 84, 1, 5 7 , 6 1 ,8 5 , E 6 , 1 4 0 ,1 7 5 , 2 1 4 , 2 2 6 , 2 8 02,8 5 , 3 3 3 , 7 9 4 , 948, 4 1 1 , 4 r 4 , 4 6 4 , 4 7 6 , 5 1595,6 ,5 5 7, 5 5 9 ,5 6 3 ,7 8 6 , 7 8 ,77 8 9 , 1017,1082,1162,1167,l168, 1232,1263,1268,1280,1283,1304, 1326,14901 T45. Od(i UnivslentFunctions (classS or classE) , 3 C ) , 3 3 6 , 3 3 9 ,3 8 8 , 4 0 5 ,4 2 6 ,M 9 , 4 5 8 , 5 2 4 , [ 1 2 8 ,2 5 2 , 2 6 9 , 2 9 1 546,747,802, 896, gO4,972,1c20,1040,1155,1200,1325,1339, I 4001 T46. Invariant (angular, sphericcl) Derivative. 1279,507, 876, 894, I 163, 1507J T47. Convolution.(Flrttung) of Functions. Hadamard Product. 926,955' 14, 102,116, I 39, 272,300,302,M, 450, 573,729,9C5, . 5 l , 1 3 2 5 ,l 4 0 l , 1 4 0 9 , 1 5 3 6 j 1 a 3 2 \, 2 4 5 , 1 2 4 6 ,1 2 4 9 , 1 2 5 0l 2 T48. Schticht (or other properties) in an Annulus1008' 12,150, 327, 470, 471, 730, 770, 792,894, 895, 976, 978, 1 5 5 6 1 , 1 4 8 , 1 3 6 4 1, 3 7 3 , 1 3 7 41, 4 2 8 ,1 4 j 4 , 1 4 6 7 , 1 1 3 6 ,1 1 4 7 1 T1g. SpecialGeometry of Map (such as k-fold symmetry). , 5 3 ,1 7 0 , 1 g g , 2 2 1 , 2 4 5 , 2 9 1 , 2 9 5 . 2 9 9 , 3 0381,7 ' I 4 0 ,4 7 , 5 4 , 1 1 0 1 , 2 , 5 1 3 , 5 1 6 ,5 2 1 , 5 3 15, 1 9 ' 3 4 0 ,3 6 3 , 3 9 13, g 4 ,3 g 7 ,4 3 1 ,4 3 2 ,4 3 3 M 6 2 2 ,6 7 3 ,6 9 4 ,7 4 4 ,7 4 5 ,7 4 7 ,7 7 4 , 7 8 1 7, 8 2 , 7 8 58, 3 8 ,8 5 3 ,8 6 5 ,9 0 1 ' 9 0 3 , 9 1 4 , g 3 4 , , 9 3 g5 3, g , 9 4 , g 5 7 , 9 7 4 , 9 g 7 , 1 0 3 41,0 4 0 ,1 0 9 3, 1 1 7 7' , , 5 5 4 ,1 5 5 9 1 1 2 1 3 , 1 2 5 4 , 1 2 5154, 3 5 , 1 4 3 71, 5 3 5 , 1 5 3 71, 5 5 1 1

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26s

p-valentFunctionscf Topic 14' T50. coefficient Bounds (reldiioits)for 869, 1103' 15081 1282,550,670,803,807, 866, Tvpicatil'-RealF-unctionscf T51. Coefficient Bounds (reiations)Jor Topic 13. [151,628,819,820,821,9M,1207,1236'1237',12471 odd u riivotent Functions o'f T 52 coeffi,'ient Bounds (relatians)foi' ToPic 45. t405, 426,9M, lL'721 T53.FgberPolynotnigls(Grunskycoefficients). [ 1 0 , 1 3 , 2 9 , 1 3 6 , 2 9 6 , 3 0 4 , 3 0 6 , 3 0 7 ' 3 0 68 0' 350'6,90' 8 3 '36, 11 'l,' ,369137' ',6, 31985' ,' , 3 9 6 ' , 4 0 6 , 4 2,14 2 2 , 4 2 4 , 4 2 5 , 4 8 3 , a g i g , 5 8 9 , 5 9 0 ' 655,676,677,721,737,749,762,768'770'798',811',8r2',814',816', 8 2 4 , 8 4 5 , 8 5 4 , 8 g 7 , g 4 g , 1 0 2 0 , 1 0 6 4 ' 1 C 6 5 ' 1 0 6 7 ' , 1 0 6 l8l'5, 1l ,0 6 9 ' , 1 0 7 0 ' 1 0 9 6 |, 0 9 , 71, 1 0 0 ,| | 2 3 , 1 0 7 3 |, 0 7 4 , 1 0 7 5|,0 g 2 , 1 0 9 3 1, 0 9 5 , , 369, | 2 7 , 7|,3 6 7 ,1 3 6 8 1 1 1 6 0 |, 2 3 0 ,| 2 6 9 ,| 2 7 0 . ! 2 7 2 ,| 2 7 5 ,| 2 7 6 , 1 4 2 3 , 1 4 7 9 , 1 4 9 l55,l 5 l Functions of the Class S" T54. Coefficient Bounds (relations) -for f(z)_-;io,,'+...AnalyticandUnivalentinlzl< [13,14,21,49,6',7,107,108,113'l2g'l5z'1 6 7 ' , 1 6 9 ' 1 ' ,4 7 15 9' ,'2 r 2 ' , 2 4 3 ' n ,2 : , 3 3 3 , 3 3 8 , 3 5 93' 5 0 '3 9 1 '3, 9 5 ' 3, 9 6 ' , 4 0 5 ' , 277,281,306,308 504' 4gl, 4g3' 498' 499' 500' 501' 5A2'503' 422,425,445,485,48;6', 647 623',625',630', ',648',649', 505,506,509,554,589;594,601'611' 6 5 5 , 6 5 6 , 6 7 3 , 6 7 4 , 6 8 5 , 6 9 3 , 7 3 5 ' 7 4 9 ' 7 7 1 ' 8 1 1 ' , 8 2 2 ' , 1068, 829',845',865' ' g03,g04, gl4,g44,looa, rciaL 1056,1064,1065,1066,106'7 1069,1070,1071,|072,|073,|074,1075,1095,1096,|097,1154, , 3 0 6 '1 3 6 5' 1 4 0 2 '1 5 1 8 1 1 1 5 5 ,1 1 5 6 ,1 1 7 0 ,1 2 2 6 ;1, 2 7 0 ,1 2 7 2 1 Functions)'[None] T55. ContinuedFractions(appliedto Schlicht of positiveReal Part of ropic 2' T56. Distortion TheoremsJor Functictns [ 3 3 , 9 1 , 1 4 7 , 2 2 4 , 2 5 6 , 2 6 5 , 2 ' 6 ' , 7 ' 2 6 8 ' 723', 3 7 6 ' 3 8 7 ' , 4 5883', 0 ' 5 2885', 2',523',524', '679''680', 831',833', 542,62'1 ,631, 640,643,644,651 8 8 7 , g | 2 , 9 5 0 , 1 0 5 0 , | 0 7 6 , 1 0 7 8 , 1 0 8 6 , 1 0 8 8 , 1 1 1 9| 3, |5| 7, 2, 103, 18 11 9, 8 ' 1 3 5 ] l |, 3 5 2 , | 2 2 | , | 2 g 0 , | 2 g | , t 2 s 2 , 1 2 9 4 |, 2 g 5 , 1 2 9 8 , | 4 7 . 71, 5 2 8 , 1 5 2 91,5 3 4 , 1 3 9 6 .1 4 1 5 , | 4 | 6 , | 4 | 9 , | 4 2 0 , | 4 4 0 ,| 4 6 , '7 1541 , 1 5 4 2 ,1 5 6 2 1

ti

266


T57. (JnivalenceOver Regionsother than the Unit Disc. [24, 25, 50, 55, 65, 120,326, 382,390,477, 597,760,986,1284, 1379,t42ll T58. Distortion Theoremsfor Meromorphic Functions of Topic 9. u l , r 3 4 , 4 9 0 ,5 3 5 , 5 9 5 , 7 0 8 , 9 3 4 , 9 3 5 ,9 3 9 , 9 4 0 , 9 5 0 ,9 5 1 , 9 5 2 , , 5 1 9 ,1 5 4 6 , , 4 7 5 ,1 4 7 6 1 , 1 5 8 ,1 2 4 3 ,1 4 1 9 ,1 4 3 6 1 1 1 1 2 1, 11 3 , 1 1 5 5 1

ts47l T59. Related Resultsfrom Analytic Funuion Theorv. [This topic is noi:being used.] T60. Multiply-ConnectedRegions. [ 5 6 , 8 8 , 1 2 1 , 3 2 8 , 3 7 9 , 3 8 39, ' 1 5 ,1 1 4 6 ,1 4 3 1 ,1 4 3 3 ] T6l. Distortion Theoremsfor Bounded Functions of Topic 22. 132,91, 213,236,265,295,297,308,351,3E8,418, 431,432,433, 854,883,891,895,904,1037,1050,1052.1078, 434,453,496,8C6, 1163,1165, 1229,1233,1262,1290,1298,1357,1381,i516, 15281 T62. Boundary Behavior (rate of growth of coefficientsor of functionals). 1 2 6 , 6 6 , 7 4 1, 2 6 ,1 2 9 ,1 5 l , 1 6 2 ,1 8 l , 1 8 9 , 2 1 0 , 2 r 2 , 2 2 1 , 2 3 4 , 2 7 9 , 3 ,5 2 , 3 5 4 , 3 6 13,6 5 ,3 6 7, 3 6 8 , 3 6 9 , 3 9 03, 9 1 ,4 1 5 , 287,332,349,351 4 1 6 , 5 3 85, 5 3 ,5 6 2 , 5 6 6 , 5 6 7 , 5 8 15,8 2 , 5 8 75, 8 8 ,5 9 0 ,5 9 6 ,5 9 8 ,6 2 0 , 6 3 8 ,7 0 5 ,7 9 7 , 8 0 28, 0 5 ,8 5 7 ,8 6 1 ,8 6 3 ,8 / 0 , E 7 1 , 8 7 2 , 8 7 4 . 8 7 6 , 8 9 8 ' 899, 900, 902, 925, 947, 956, 958, 960, 1027, 1029,1037, 1038, 1039,1043, 1046,1085,1099,1102,1124,ll6y',1167,1253,1322, 1434,1437,11i3, 1474,i475, 1476,i506, 15301 T63, Distortion Theoremsfor Starlike Functions cf lopic 6. [30, I 26, 13l, 163,191,I 92, 194,230,253,269,347, 377,388, 458, 4 5 9 ,5 2 4 ,5 4 3 , 5 8 76, 1 6 , 6 1 9&, 3 , 6 5 8 , 7 7 5 , 7 7 6 8, 0 2 , 8 5 78, 5 8 ,8 8 8 ' 9 1 2 ,1 0 0 9 .i c 8 - ? ,i c 8 5 , l i z z . 1 2 4 8 ,1 2 5 0 ,1 2 9 7 , 1 3 0 i .1 3 1 9 ,1 3 2 3 , 1335,1348, 1349,1350,1386,1387, 1416,1419,1474,1475,1500, l 5 l l , 1 5 2 7 , 1 5 3 3 , 1 5 3 71,5 4 3 ,1 5 5 8 1 T&. Di,stortion Theoremsfor Convex Functions of Topic 10. 619' [30, 139, 143,14, 145,147,194.247,252,266,388,479,543,

r

s

TOPIC REFERENCES

261

1250, 7 g 5 , 8 9 1 , 9 0 5 , 9 0 g6 |, 2 , 1 0 5 9 ,1 0 8 5 l, l 1 g , | | 2 0 , | | 2 2 , | 2 4 8 , 1 3 1 9 ,1 3 2 1 , 1 3 2 31, 3 3 5 ,1 3 5 3 ,1 3 8 2 ,1 4 9 1 1 Topic 14' T65. Distorticn Theoremsfor p-valent Functions o-i [ 8 C 3 ,8 0 7 , I 3 7 3 ] of Top;g 13' T66. Distortion Theoremsfor Typicatty-RealFunctions [ i 7 8 , 8 2 0 , 1 c o 5 ,l l l E , 1 2 0 i , 1 5 4 ( ) ] of Topic +5' T67. Distortion Theoremsfor Odd Univalent Functions 1252,368,458, 5241 - z+ S: T68. Distortion Theoremsfor Functions of the Clqss fQ) ezzz+ . . . Analytic and Univalentin lzl 266,2ll, 321,336' 338' 339', 147,74, 109, t34. 212,,222,241, 265, 5 3 5 '5 5 4 ' , 3 7 g , 3 8 33, 9 6 , 4 3 7 , 4 5 84, g 0 ,4 g 3 ,5 2 5 ,5 2 8 ,5 2 9 , 5 3 15' 3 3 ' 8 6 4 ,9 0 5 ,9 | 4 , , 5 7 9 , 5 9 56, 1 3 , 6 2 2 , 6 3 0 6, 7 | , 7 2 4 , 7 3 87, 4 | , 8 2 9 . 8 4 6 , 1 2 0 0 ,| 2 | 3 , 9 5 1 , ) ( , 9 , 1 0 5 0 ,| 0 7 7 , 1 1 1 0 ,1 1 1 9 ,1 1 5 5 ,1 1 5 9 ,1 1 6 3 , 15011 1 2 1 8, 1 2 1 3 , 1 2 4 8 ,1 2 6 7 , 1 2 8 21, ,3 2 2 ,1 4 3 6 ,1 4 3 7 , 1 4 3 9 , 1 4 9 3 ' and T69. u-Convex, ..-Starlike Functions (Mocanu functions) Generalizations. 3 1 8 '3 5 3 '3, 5 5 ' [ 3 3 , 3 5, 9 5 , 9 7 , 9 8 ,l N , 1 0 5 , 2 3 9 , 2 8 9 , 2 9 0 , 2 9 1 , 2 9 3 ' g0 0 ,g ,g 3 5 ,9 5 8 ,9 5 9 , 9 6 1 , 9 6 6 , 9 6 7 , 9 6986' 9 ' 3 5 g ,7 7 7 , 7 i 7 8 , " 1 7 g , 7 g gg7,ggg,ggg,1000,1001, 1002,l00l , 1197,1195,1337' gg0, 996;,, 1342,l4l'7, 14181 T70. Bazitevii Functiores(and generalizations). 6 9 4 , 7 7 9 , 7 8 08' 0 8 '8 4 7' 9 3 1 ' 12,216,2lg,28g,2g0,2g3,353 65 , 8, 1055,1178, 956, 969, gg7, 1003,1004, 1006,1040, 1051,1054, 1 4 4 6 '1 5 1 2 1 l l 7 g , 1 l 8 l , l l g 4 , 1 2 4 6 ,1 3 2 4 , 1 3 5,5l M 3 , l M , T7 | . Functionso-fBoundedBoundary Rotation. g, 288,292,293' 340' 494'7M' ll7, 78, 172, 173, 177, 17 214,286, 965'970' 7 0 6 , 7 0 7 , 7 7 4 , 8 0 2 ,8 0 4 , 8 0 5 , 8 0 9 , 8 6 i , 8 7 5 ' 8 8 2 ' 9 6 0 ' 1 0 5 5 ,1 0 9 0 , 1 0 1 4 ,1 0 3 5 ,1 0 3 6 ,1 0 3 8 ,1 0 3 9 ,1 0 4 0 ,1 0 4 1 ,l M 3 , | 0 4 7 , 1274, 1113 , L l z l , 1 1 2 4 , 1 1 2 5 l,l 9 5 , 1 2 1 4 , 1 2 1 5 , 1 2 2 3 , 1 2 2 5 , 1 2 7 3 ' 1 3 4 1 ,1 3 4 3 ,1 3 4 5 ,1 3 8 8 ,! M 5 , 1 4 6 5 ,l 4 7 l l

26E


T72. Distortion Theorems Involving Coefficients (various classesof functions). I 3 2 , 9 1 ,3 8 8 ,M , 4 4 8 , 4 4 9 , 8 4 6 , 8 8 3 ,8 8 4 ,8 8 7 ,1 0 8 5 ,1 2 5 8 , 1 3 5 7 ,

r4371 (of various classesof functions). T73. Rodiusof Close-to-Convexity l9l, 142,214,221,222, 292, 340, 453,460,699,7 46,776, 802, 855, 858, 1033. 1076,1084,1124,1227,1352,1353,15431 T74. Distortion Theoremsof Close-to-ConvexFunctions of Topic 5. [194, 252, 440, 442,M3, 446,838, 912, 1085,1149,1178,1249, 12ffi, 1323,1327,1333,1340,15021 T75. Coefficient Bounds (relations)Jor Close-to-ConvexFunctions of Topic 5. t 1 1 3, M 0 , M 3 , 4 4 6 ,4 5 6 ,5 2 4 ,5 4 6 , 5 4 8 ,5 8 8 , 6 9 3 , 8 6 7 , 9 1 2 ,1 1 4 9 , 1219,1327,1333,1340,15021 T75. Distortion Theo,'emsfor Functions of Bcunded Boundc,ryRotatiort of Topic 7l. 1 1 7 2 , 2 8 32, 9 3 , 3 4 0 ,7 0 7 , 8 0 2 , 8 0 5 1, 0 1 4 ,1 0 3 5 ,1 0 3 8 ,1 1 2 5 , 1 2 2 3 , 1273,1343,14451 T77. Coefficient Bounrlsfor Functions of Bounded Boundary Rotation of Topic 7l. Ir72, 173, 177,286,288,340, 706,774,802,804,805,875, l0l4' 1035,1036,1038,1047,1090,1125.1223,1273,1274,1345,14/5,

r47ri T78. Distortion Theoremsfor Functions Convex in One Directicn of Topic 41. 1524,57l, 572, 1235,l30l l T7g. Coefficient Bounds for Functions Convex in One Direction of Topic 41. , 2 2 3 ,l 3 0 l l t l L 3 , 5 2 4 , 5 7 1 , 5 7 2 , 6 2 8 , 9 7 21, 2 1 9 ,1 2 2 C 1 T80. Distortion Theoremsfor Bazilevic Functions of Topic 70.

,J

TOPIC REFERENCES

269

[847, 1006,1051] BazilevicFuncticns of ropic 70' tgr. Coefficient Rounds(rerations)for 1446] [358, 694,956,1006,|M:J, cf {JnivqlerfiFunctions' Tg2. Linear ccmbinations, Products, 1 3 2 . , 3 6 , 9 1 , 1 4 2 , 2 0 5 , 2 1 ! , 2 1 4 , 2 4 8 , 2 6 9 ' 3 58 1'440',446',451',460', 8 5 5 ' , 5 9 ' i,0 1 8 ' ,1 0 3 3 ' , 4 6 8 , 4 7 5 , 4 7.7 5 2 6 ,5 5 ? , , 6 7 8 , 7 1 5 , 7 g 5 , 8 3 ? ' 1355 , \ 3 5 7 ,1 3 6 1 ,1 3 9 6 , 1 0 8 9 ,l 1 0 9 ,| 2 2 7 , | 2 4 1 , | 2 6 4 , | 3 3 4 , 1 3 3 8 , 1400,1469,1526,1536,1542,15481 'Topic (a-starlike) Functions of a-convex Theorems for Distortion Tg3. 69. 1,342,I 5481 1291,293,777, 958, a-CotNex (a-stariike)Functions Tg4. coefficient Bounds (rerations)for of ToPic 69. 1291,358,777,778,77g,780,966,1417'1418'15481 T85. Univalenceof Integrals' 134,71,72,g1,94,95,gg,102,105'139'147',142',203'205'214' 2 2 4 , 2 2 8 , 2 4 8 , 2 5 g , 3 5 7 , ' 5 2 7 , 6 9 7 ' 6 9 8 ' 7 4 6 ' , 8 2 8 ' , 9 0 61' ,395235' ,' , 9 2 8 ' , l 2 3 l ' 1 2 9 7 '1 3 0 1 ' , 1 0 5 0 ,1 0 5 2 ,1 0 5 3 ,I I I 1 , I I 2 4 , l l g g ' 1 2 2 7 ' 1 3 5 5 ,1 5 4 1 , 1 5 M , 1 5 4 8 ,l 5 6 l l (and related classes) Tg6. Distortion Theoremsfor Bieberback-Eilenberg Functions of ToPic 34' 646,651] [ 9 , I 1 , 1 5 , 1 3 8 ,5 0 9 ,5 1 1 , Bieberbach-Eilenberg(ond Tg7. coefficient Bounds (relotions) for Functions of Topic 34' related classes) , 1 1 , 5 1 2 , 6 0 8 1, o 2 U [ 1l , 1 5 ,5 O 9 5 T88. ExtremePoint TheorY' [182,186,187,188,18g,2'73,284'387'500',541',542',s4y'.',545', 546,547,548,550,551,574,575,576'577'578',585',709',807',912' 9 1 3 ,9 1 6 ,g 4 2 , 1 2 4 9 , 1 3 3 51,3 3 6 '1 3 4 0 1


210

T89. Functions of Bounded Index' [40] , 402, 403, 699, I 187] T90. Entire Functions.

1192,1243,1302,1304,1306,

[400, 404, 406, 5'19,699,817' 1029, , 3 1 0 ,1 3 1 l ' 1 3 1 21, 3 1 51, 3 1 61, 3 1 7 1 13071 , 3 0 8 ,1 3 0 9 1

TABLE 1 which Following is a list of those referencesin this bibliography in included rrot were were publishedPrior to the Year 1966and which BibliographYI. Year

References

1950 1955 1959 I 960

u 4841 u 4851 12551 u059,1060,

r95l 1962 1963 t964

i965

[ 3 4 17, 8 1 ,1 3 2 81, 3 6 61, 5 1 6 1 1782,982,14861 , t{3 ,877,1378J u 4 9 , 1 5 0 , 3 7 2 , 6 2 i6, 4 5 7 758,782,784,785, [ 3 7 ,81 , 2 3 4 , 3 0 03, 1 2 , 4 9 86, 7 0 , 7 3 1 , 7 4 1 , 9 8 3 ,r l l 7 , 1 1 6 91, 2 0 8 1 , 52,759.786,'187, 07 , 67 u , 3 8, 4 5 , 1 4 8 , 2 3 53,1 0 ,3 7 3 , 4 1 4 , 6 5 6 1212,1256, , g o s ,8 7 8 ,9 4 7 , 9 8 49. 8 5 ,1 0 1 1 1, 0 6 1 , 1 1 4 6ll';3, 1257,1380,1427,1436,15461 2',76,31l,330, 374,375', 14,39, 42, 51,58, 66, 127, l-28,236, 68i' 4 1 7 , 4 2 4 , 4 3 6 , 4 6 5 , 4 g g , 55 01 03 , ,5 1 6 ,6 1 5 ,6 3 6 , 6 4 6 , 6 7' 7 837' 684, 716,736,7 53,7 55,788,790,825,826,827,828, 836' 9'.19' 842,843,851,866, 867,87g,903,972,975, 976,977,978' ll3i', i l05, 980,986, 1034,1064,1076,1077,1078,1093,1094, l23l' I l - ? 8 ,I 1 4 9 , 1 1 5 0 ,I l 5 i , 1 1 7 4 ,l l 3 2 ' 1 l 9 E, i 2 0 9 , l 2 l 9 ' L42l' 1419, 1264,lz]t, t2l2:, izig,l28l, 1365,1381, 1392, |487, | 4 2 8 , | 4 2 q 1 4 3 0 ,| 4 4 7 , | 4 4 8 , t + l g , 1 4 5 0 ,l 4 5 l , | 4 5 2 , , 5 5 1 ,t 5 5 2 . 1 5 5 3 1 1 4 8 8 ,1 5 5 0 1

A

TOPIC REFEP.ENCES

211

TABLE 2 which Following is a list of those referencesin this bibliography publishedduring the year 1975' $,/ere 3 5 7 , 3 g 7 , 5 4 85, 4 9 , 5 5 05, 7 8 ,5 8 0 ' 5 9 4 ' u 1 6 , 1 5 3, 2 1 6 , 2 ' t 8 , 2 7 2 , 2 g 0 , 3 3 3 , 10|.',1 ! 50' 9 9 ' 6 5 2 , 6 8 05, 9 1 , 7 0 8 , 7 3 g , 8 2 2 , 8 4 9 ,8 i 4 , 9 1 6 , 9 4 3 , 9 6 4 , 9 6 5 ' , 3 4 0 ,1 3 4 3 ,1 4 1 0 ,1 4 3 9 ,i 5 4 4 ) 1 1 8 4 ,1 2 6 2 ,i 3 0 5 , t 3 3 € . 1

TABLE 3 this Following is a listing of the total number of researchPaPersin bibliographywhich were publishedin eachof the given Years. Year

Total Number of PdPers

1966 lvo/ 1968 r969

r23

r970 197|

r972 r973 t9'14 t975

110 107 130 t46 t49 160 166 IM t25

272

B IBL IOGR AP H YOF SC H LIC H T FU N C TION S

TABLE 4 Followingis a list of Math. Review(MR) numbers(which had not in beenavailableat time of first publication)for someof the References the Bibliography,Part II. Ref. 17

MR# Ref. MR54 #2939 186

MR# Ref. MR53 #5849 332

MR# Ref. MR52 #8407 519

MR53 #5845

MR#

23

53 3297

194

53 788

345

52 11029 547

53 I1036

36

53 3288

20s

57 9950

3s9

53 3286

548

53 11036

37

54 528

222

54 7768

360

56 r2250

594

53 792

53 801

234

52 I l03l

366

52 t4259

632

54 2946

'/6

tt?

79

53 5848

258

3314

367

52 l 1030 678

52 1426r

87

54 5456

264

54 545I

370

57 t2837

52 t427|

153

54 525

271

53 8427

400

52 l 1039 720

57 r2839

r66

52 r42s8

303

53 l iu31

451

57 3372

54 54s7

175

54 537

320

52 ! l02r

496

53 I1043 776

780

52 14266 965

52 t1024

52 1262 it027

53 1376 5844

803

53 l1038 l0l8

52 53 t4263 1270 8409

52 r4265

805

52 53 r4268 1022 5846

822

52 t4267 1043

835

53 3282

54 2943

52 1090 rr025

707

758

t377

53 l1037

53 58 1280 22527 1388 3290 l3t8

54 5465

55 1425 r0662

1326

54 5479

53 1465 13549

TOPIC REFERENCES

MR# Ref. MR# Ref. 58 52 849 t4262 I 1 6 6 I 1 0 1 i 3.36 52 54 1358 11026 1 181 859 13057 53 53 1362 5847 I 1 8 3 862 I 1040 52 55 1 1032 1363 1 2 0 8 653 896 56 54 137| s862 554 1250 963

Ref.

MR# 54 294J

Ref.

MR#

53 1433 8 4 1 0 53 53 8429 1530 11041 52 r42& 53 8408

153I

54 2948

r532

53 3287

56 5857

Corrections

Reference 385 607 618 692

sameas

Reference 384 604

6r7 126

is Todorov' Pavel Notes (a) Reference1094: author Pletneva'T . G . (b) Ezroh;, T. G. is sameauthor as

LIJ

274


BIBLIOGRAPHYOF SCHLICHT FUNCTIONS 1) Part III (1976-198

CONTENTS Preface Bibliography Prior to Year 1976 Table l. References in Year lg82 2. References Table Table 3. Number of ReferencesPublisher!Each Ycar Corrections.

. 275 276 351 352 .,*352 353 .,i.

;,

J{

-

PREFACE

215

PREI.-ACE

tc contains1025references Dib'ography of SchlichtFunctions,Part III, (Schlicht)and multivalent publicationsin the theory of analyticunivalent through r981 and is a continuafunctions.part III coversthe ),ears19'76 Parts I' II' describedin tion of Bibliography of Schiicht Functions, earlierpages. and which werenot inSomePapersPublishedPrior to the year 1976 I. Somepaperspublishedir cludedin Parts I, II are now listedin Table numbers(MR) are inthe vear 1982are listedin Table II' Math. Review cluded for most references' Abstractshavebeen Part III differs from Parts I,II in two respects' and cross-indexlistingsare omitted and also no subtopic crassification justified becauseof their included. The omission of abstractsis easily results in the theory of transient value. classification of the various are usedin Part I' 90 subSchlichtfunctionsinto subtopics(68 subtopics and betweenreferences topics are usedin part II) and cross-indexlistings of hundreds task requiring subtopicsis a very valuablebut monumental prior to the publication hours of work-precious time not available deadlinefor Part III. S. D. Bernardi July 1982

t

216

BIBLIOCRAPHY OF SCHLICHT FUNCTIONS

BIBLIOGRAPHYOF SCHLICHT FUNCTIONS (Part III) Sect' III 1. Abe, H. On some analyticfunctions. Mem. Ehime univ.

7 (t97|t,tro.4,tff-IQI: MRK lzk77. Engrg.

2. Abe. H. On multivalentfunctions in multiply connecteddomains.l. Proc. JapanAcad. 53 (1977),no. 3, 116-ll9; MR 56 #594. 3. Abe, H. On multivalent functions in multiply connecteddomains' lI. Proc.JapanAcad. Ser.A lvIath.Sci.53 (1977),no.2,68-71;MR 58 #6210. 4. Abiarr, A. The coefficients cf the Laurent expansion of analytic -functions.Arch. Math. (tsrno) 13 (1971),no. 2, 65-68' 5. Abian, A. Hurwitz' theorem implies Rouch€'s theorem. J' Math' A n a l . A p p l . 6 l ( 1 9 7 7 )n, o . 1 , 1 1 3 - 1 1 5 . 6. Abian, A.; Johnstotr,E. H. Zeros of partial sums of the Laurent l' seriesof anatyticfunctions. KyungpookMath. J. 2l (1981),no' 87-90. 7 . Abu-Muhanna, Y.; MacGregot, T. H. Variabitity regions for by bounded analytic functions wi;th apptications to families defined

FUNCTIONS (PAI(T iII) BIBLIOGRAPHY OF SCHLTCHT

271

subordination.Proc.Amer.MathSoc.s0(1980),22-l-213;MR 8 1m:30022. points of families of g. Abu-Muhanna, y.; MacGregor,T. H . Extreme 176 to cont'ex mappings' Math' Z' analyticfunctions subord;nate ; R 82d:3C02i' ( I 9 8 1 ) ,n o . 4 , 5 1 1 - 5 1 9 M T. H. Families of real and SymMacGregor. g. Abu.Muhanna, Y.; no' Amer' Math' Soc' 263(1981)' metricanolytic functions.Trans. l , 5 g - 7 4 ;M R 8 2 a : 3 0 0 1 1 ' mapping' inequalityinvoh'ingconformal lc. Acker, A. An isoperimetric g77)' no' 2' 730-234;NIR 57#3364' (1 Proc. Amer. Math. Soc' 65 Nores, in un'ivarent functiorts. Lecture ,,. AharonoV,D. speciar toiiri ' UniversitYof MarYland(l 971) A minimal-qreaproblem in conforS' lZ. AharonoV, D.; Shapiro, H' of the Symposium on complex mal mapping. (Abstracti-eroc. _ 1973,pp. i-5' London Math' canterbury, Kent, uni". Analysis Soc.LectureNoteSer.No.|2,CambridgeUniv.Press,London (]j7$; MR s4 #526' A short proof of the Denioy coniecture' 13. AharonoV,D.; Srebro,v. B u l l e t i n ( N . S . ) A m e r . N i a t n . S o c . 4 , n o . 3 ( M a y 1 9a3 8 1 ) . aq of a betweenthe coefficients and 14. Ahlfors, I- V. An inequality (1976). Soc. Transl. (2) vol. 104 univalentfunctiot,. Amer. Math.

pf;r:l;ltt. r5.

of fyn:t:::: ':i'!,"!l^'n,the unit disc' certainctasses

5 (1971)'Do' Z' 3'79-389' Bull. Inst. Math' Acad' Sinila tvith on stsrtike and convexfunctions K. P. Jain, ?.; o. Ahuja, 16. (2) 3 Bull' MalaysianMath' Soc' missingand negativecoefficienfs' ( 1 9 8 0 ) ,n t . 2 , 9 5 - 1 0 1 ;M R 8 2 d : 3 0 0 1 3 ' value solvabitityof inverseboundary l7 . Aksent'eV,L. A. The u-nivale'tt 4)' (1 Kraev' zadacam vyp' I I 97 problems. (Russian)Trudy sem. 9 - 1 8 ;M R 5 7 # 6 5 2 '

1 8 . A k s e n t , e V , L . A . ( ] n i v q l e n t c h a n g e o f g76),30-39; p o r y g o n a l rMR J.om ins.(Russian) 58a#22522' 13il zadacamvvp. Kraev. Sem. Trudy 1 9 . A k s e n t , e v , L . A . ; G a i d u k , V . N . ; M i k kproblem a , V . P . T h eau regular n i v o l efunc' nt for value boundary inverse the of solvability (Russian)Trudy Sem' Kraev' tion in a doubly connectedregion ' -8; MR 56 #15948 ZaaacamVvp' 12 (lg7 5)' 3 z 0 . A k s e n t , e v , L . A . : K u d r j a s o v , s . N . S o m e c o n dvarue i t i o nproblem s f o r t h efor inverseboundary univarenceof the sorution'ofan Vyp' 6 f1$V Sem' Krle-v' Zadacam a symmetricprofite' tnt"iunl (1969),3_15.Foru,.ui.*olthisitemseeZbl236#76007;MR58

# r 7l r 3 .

zIEBIBLIOGRAPHYoFSCHLICHTFUNCTIONS

of some 21. Al-Amiri, H . s. Applications of the domsin of variability (Polish and functionals within the classof Caratheocloryfunctions. Sect.A Russiansummaries)Ann. univ. Mariae curie-Sklodowska ; R 81e:30019' 3 l ( l 9 7 7 ) , 5 - 1 4( 1 9 7 9 )M Rev' 22. Al-Amiri, H. S. Certain anulcgy of the a-convexfunctions' MR 80i: RoumaineMath. PuresAppl.23 (1978),no. 10,1449-1454; 30017. in the 23. Al-Amiri, H. S. Certain nth order dif-ferentialinequqlities MR complexplane. canad. Math. Bult. 2l (1978),no. 3 ,273-277; . 80m:30002 within the 24. Al_Amiri, H. s. The domain of variobitity of afunctional summary) classof univolent starlike fuitctions. (Scrbo-croatian 81e:30018' G l a s .M a t . s e r . I I I 1 4 ( 3 4 )( 1 9 7 9 )n, o . 1 , 5 5 - 6 6 ;M R prestsrlike functions' J' 25. Al-Amiri, H . S. Certain generqlizationsof MR Austral. Math. Soc. Ser. A 28 (1979), no. 3, 325-334; 81b:30018. Ann. Polon. Math' 38 clerivatives. 26. AI-Amiri, H. S. On Ruscheweyh ( 1 9 8 0 )n, o . 1 , 8 8 - 9 4 ;M R 8 2 c : 3 0 0 1 0 ' 27. Al-Amiri, H.; Mocanu, P. T. certain sufficient conditions for gnivslencyo,f the classc'. I. Math. Anal. Appl. 80 (1981),no' 2, 387-392;MR82g:30033. Proc' 28. Al-Amiri, H.; Mocanu, P. Spiratlikenonanalyticfunctions' 5 ;R 8 2 j : 3 0 0 2 8 . A m e r . M a t h . S o c . 8 2( 1 9 8 1 ) , 6 1 _ 6 M in the theory of continustions 29. Aleksandrov, I. A. Parametric (1976)' 343 pp' univalent futnctions. Izdat. "Nauka," Moscow 2 . 0 8 r ;M R 5 8 # 1 0 9 9 . equation' 30. Aleksandrov,I. A. A caseof integrction of the Lowner MR (Russian)sibirsk. Mat. z. 22 (1981),no. 2, 207'209, 238; 8 2 f: 3 0 0 1 7 . problemsfor svstems 31. Aleksandrov,I. A.; Andreev,v . A. Extremal Sibirsk. Mat' Z' 19 (Russian) of functions without common vqlues. ( 1 9 7 8 )n, o . 5 , 9 7 0 - 9 E 2 ,l 2 l 3 ; M R ' 8 0 d : 3 0 0 i 8 ' conJormollymap 32. Aleksandrov,I.A.; Cvetkov,B.G. Functionsthat no' I '4-25' the strip into itsel,/.(Russian)Sibirsk.Mat. Z.2l (1980), 235. properties-of 33. Aleksandrov, I. A.; Mandik, v. P. Extremal 7" 2 simultoneouslyp-valent fuiictions. (Russian) Sit irsk. Mat' (1981),no. 4, 3-13,229;MR E2i:J0028' A.optimal t:!' 34. Aleksandrov,I. A.; Zavozin,G. G.; Kopanev,s. (Russial) Dif' trclsin coefficientproblernsfor univoteit ,frmcticns. 771; MR 54 ferencial'nyeUravnenijal? (1976),no. 4, 599-611, #536.

(PART III) BTBLIOGRAPHYOF SCHLtcHT FUNCTIONS

219

generalizedareas in the case oJ 35. alenicyn, J. E. Inequaiities for with circular cuts' multivalent conforrnal ,ropping't of domains (Russian)Mat.Zametkizg(19E1),no.3,387-395,479;MR . 629:3C040 o-fa form o-fa multiply connected 36. Alenicyn, J. E . On the !eastareL (Russian)Mat' of p-sheetedcoriformal mappings' dontqin in cr clas.s ' Zametki30 (1981),no' 6, 807-812'95'1 problems Brarrnan'D. A. Research 37. Andersofl,J. lr4.;Baith, K. F.; Math' Scc' 9 (19'77)'llo' 2' in camplex anal.vsis.Buli. London 1 2 9 - 1 6 2M ; R 55#12899' Hypernorma! meromorphicfunc' 3g. Arrderson,J. M.; Rubel. L. A. no' 3, 301-309;MR 80b:30026' tions.HoustonJ. Math. 4 (1978), L' Coefficient multipliers of Bloch 39. Anderson, J. M.; Shields,A' f u n c t i o n ^ s . T r a n s . A m e r . M a t h S o c . 2q2certain 4 ( | 9 7 6crdss ) , n oof . 2functions ,255.265. 40. Andreev, \,. A. Extremistprobiems for disc. (Russian)Dokl' Akad' that are regular snd bctriaed in the N a u k S S S R z z s ( 1 g 7 6 ) , n o ' 4 ' 7 6 9 - 7 7 1 ; M R 5 4 # 1domains' 3 0 6 7 ' (Ruso,fnonovertapping problems certain A. v. Andreev, 41. 715;MR 55 #3235' 3 sian)Siblrsk.Mat. Z. i (1976),no. ,183-498' ond convexity of certain 42. Anh, v. v.; Tuan, P D'. on starlike:ness analyticfunctio;ts.PacificJ.Math.69(1977),no.1,1_9,MR55 #5848. p-converity of certainstsrlike univalent 43. Anh, V. V.; Tuan, P' D ' On 10' Matlr. Pures APPI' 24 (1979)'no' functions. Rev' Roumatne 1 4 1 3 -1 4 2 4 M R 8 1 b : 3 0 0 1 9 ' An extremalProblemfor univalent 44. Astahov,V. N. (Astahov'V' M') Nauk Ukrain' SSR Inst' analYtic Junctions' (Russian) Akad. Processov(1977),18-24; Kibernet.PrePrintNo' 11 Teor' Optimal.

I\{R 58 #28472. 4 5 . A s t a h o v , V . M . T h e r a n g e o f v a l u e s o . f a s y ssummary) t e m o f f u nDokl' ctionalsin (Russian,English univalent funirfoir. of c/asses MR 58 no. 3, 195-t98,284; Akad.Naukukrain.ssR Ser.A (1978), #1129 ., ' - ^t -.-i,,ntnnt on the crassof univarenr 46. Astahov, v. M . The rangeof a functionar (Rrrssian)Theory of functions and functions with rent coefiicrerrc." mappings(Russian),"NaukovaDumka"'Kiev(1979)'pp'3-27' t 74 ; I V I R8 1 d : 3 0 0 1' 3 Gutljans'kli,V..J. Someextremal 47.Astahov,V. N. (Astalrov,V.M.); (Russian)Metric quesproblems for univalent analyticfunctions' mappings(Russian)"'Naukova tions of the theory of functionsand MR 58 #28475' Dumka," Kiev (1977),pp' 3-19' 166; of on some classes 48. Atzmon, A. Extremallinrtions for functionals

2E0BIBLIOGRAPHYoFSCHLICHTFUNCTIONS

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Bibliography of Schlicht Functions

Zeta Functions over Zeros of Zeta Functions

Theory of Permutable Functions

Vistas of Special Functions

Theory of Hypergeometric Functions

An Atlas Of Functions

Computation of special functions

The Structure of Functions

Spaces of functions

Integrals of Bessel functions

Vistas of Special Functions

Theory of Permutable Functions

Computation of special functions

An Atlas Of Functions

An atlas of functions

Vistas of special functions

Vistas of special functions

An atlas of functions

Analysis of Boolean Functions

Theory of complex functions

The theory of functions

The structure of functions

Extension of holomorphic functions

Calculus of Vector Functions

Spaces of Analytic Functions

Cultural functions of translation

Rings of continuous functions,

Theory of Conjugate Functions

Integration of algebraic functions

Handbook of Mathematical Functions

Functions of Several Variables

Bibliography of Schlicht Functions

Zeta Functions over Zeros of Zeta Functions

Theory of Permutable Functions

Vistas of Special Functions

Theory of Hypergeometric Functions

An Atlas Of Functions

Computation of special functions

The Structure of Functions

Spaces of functions

Integrals of Bessel functions

Vistas of Special Functions

Theory of Permutable Functions

Computation of special functions

An Atlas Of Functions

An atlas of functions

Vistas of special functions

Vistas of special functions

An atlas of functions

Analysis of Boolean Functions

Theory of complex functions

The theory of functions

The structure of functions

Extension of holomorphic functions

Calculus of Vector Functions

Spaces of Analytic Functions

Cultural functions of translation

Rings of continuous functions,

Theory of Conjugate Functions

Integration of algebraic functions

Handbook of Mathematical Functions

Functions of Several Variables

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