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Article

Title: On an extremal problem (English)
Author: Zyskowska, Krystyna
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 120
Issue: 2
Year: 1995
Pages: 113-124
Summary lang: English
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Category: math
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Summary: Let $S$ denote the class of functions $f(z) = z + a_2z^2 + a_3z^3 + \ldots$ univalent and holomorphic in the unit disc $\varDelta= \{z |z| < 1\}$. In the paper we obtain a sharp estimate of the functional $|a_3 - \alpha a^2_2| + \alpha|a_2|^2$ in the class $S$ for an arbitrary $\alpha\in\Bbb R$. (English)
Keyword: coefficient problems
Keyword: Koebe function
Keyword: univalent function
MSC: 30C50
MSC: 30C70
idZBL: Zbl 0857.30016
idMR: MR1357596
DOI: 10.21136/MB.1995.126223
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Date available: 2009-09-24T21:09:34Z
Last updated: 2020-07-29
Stable URL: http://hdl.handle.net/10338.dmlcz/126223
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Reference: [1] L. Bieberbach: Über die Koeffizienten derjenigen Potenzreihen, welche schlichte Abbildung des Einheitskreises vermitteln.Preuss. Akad. deг Wiss. Sitzungsb. 38 (1916), 940-955. Berlin.
Reference: [2] G. M. Goluzin: Some questions of the theory of univalent functions.Trudy Mat. Inst. Steklov 27 (1949), 51-56. (In Russian.) MR 0042510
Reference: [3] Z. J. Jakubowski K. Zyskowska: On an estimate of some functional in the class of holomorphic univalent functions.Mathematica Bohemica 118 (1993), 281-296. MR 1239123
Reference: [4] J. A. Jenkins: On certain coefficients on univalent functions.Princ. Univ. Press, New Jeгsey, 1960, pp. 159-194. MR 0117345
Reference: [5] W. Ma D. Minda: Uniformly convex functions II.To appear in Ann. Polon. Math. Zbl 0792.30008, MR 1244399
Reference: [6] A. C. Schaeffer D. C. Spencer: Coefficient regions for schlicht functions.Amer. Math. Soc., Colloq. Publ. 35 (1950), 36-37. MR 0037908
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