1918

Subclasses of starlike functions related toBlaschke products

Yayın Aralığı: Yılda 6 Sayı
Başlangıç: 2002
Yayıncı: Hacettepe Üniversitesi Fen Fakultesi

In this paper we examine subclasses of the class of starlike functions defined by the setof zeros of Schwarz functions. Distortion and the growth theorems are shown. Bounds ofthe classical coefficient functionals are also computed.

PDF

___

[1]J.W. Alexander,Functions which map the interior of the unit circle upon simpleregions, Ann. Math.17, 12–22, 1915.
[2]P.L. Duren,Theory ofHpSpaces, Academic Press, New York, London, 1970.
[3]P.L. Duren,Univalent Functions, Springer Verlag, New York, 1983.
[4]A.W. Goodman,Univalent Functions, Mariner, Tampa, Florida, 1983.
[5]R.E. Greene and S.G. Kranz,Function Theory of One Complex Variable, AMS, Prov-idence, Rhode Island, 2006.
[6]F.R. Keogh and E.P. Merkes,A coefficient inequality for certain classes of analyticfunctions, Proc. Amer. Math. Soc.20, 8–12, 1969.
[7]J. Krzyż,Coefficient problem for non-vanishing functions, Ann. Polon. Math.20,314–316, 1968.
[8]A. Lecko, and B. Śmiarowska,Classes of analytic functions related to Blaschke prod-ucts, Filomat,32(18), 6289-6309, 2018.
[9]M.J. Martin, E.T. Sawyer, I. Uriarte-Tuero and D. Vukotić,The Krzyż conjecturerevised, Adv. Math.273, 716–745, 2015.
[10]R.R. Nevanlinna,Über die konforme Abbildung von Sterngebieten, Översikt av FinskaVetens.-Soc. Förh., Avd. A,LXIII(6), 1–21, 1920–1921,
[11]N. Samaris,A proof of Krzyż’s Conjecture for the Fifth Coefficient, Caomplex Vari-ables, Theory and Application,48(9), 753–766, 2003.