Abstract
References
- [1] J.W. Alexander, Functions which map the interior of the unit circle upon simple regions, Ann. Math. 17, 12–22, 1915.
- [2] P.L. Duren, Theory of $H^p$ Spaces, 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 analytic functions, 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 conjecture revised, Adv. Math. 273, 716–745, 2015.
- [10] R.R. Nevanlinna, Über die konforme Abbildung von Sterngebieten, Översikt av Finska Vetens.-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.
Abstract
In this paper we examine subclasses of the class of starlike functions defined by the set of zeros of Schwarz functions. Distortion and the growth theorems are shown. Bounds of the classical coefficient functionals are also computed.
Keywords
Riesz Theorem Schwarz functions Carathéodory functions factorization distortion theorem growth theorem starlike functions
References
- [1] J.W. Alexander, Functions which map the interior of the unit circle upon simple regions, Ann. Math. 17, 12–22, 1915.
- [2] P.L. Duren, Theory of $H^p$ Spaces, 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 analytic functions, 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 conjecture revised, Adv. Math. 273, 716–745, 2015.
- [10] R.R. Nevanlinna, Über die konforme Abbildung von Sterngebieten, Översikt av Finska Vetens.-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.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Research Article |
| Authors | |
| Publication Date | February 6, 2020 |
| DOI | https://doi.org/10.15672/HJMS.2018.649 |
| IZ | https://izlik.org/JA28MG39NY |
| Published in Issue | Year 2020 Volume: 49 Issue: 1 |