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Vladikavkazskii Matematicheskii Zhurnal, 2006, Volume 8, Number 2, Pages 50–53
(Mi vmj126)
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Inequalities for the Schwarzian derivative for subclasses of convex functions in the unit disc
Y. Polatoglu, M. Caglar, A. Sen Istanbul Kultur University, Istanbul, Turkey
Abstract:
Nehari norm of the Schwarzian derivative of an analytic function is closely related to its univalence. The famous Nehari-Kraus theorem ([3], [4]) and Ahlfors-Weill theorem [1] are of fundamental importance in this direction. For a non-constant meromorphic function $f$ on $D$ the unite disc, the Schwarzian derivative $S_f$ of $f$ by is holomorphic at $z_0\in D$ if and only if $f$ is locally univalent at $z_0$. The aim of this paper is to give sharp estimates of the Nehari norm for the subclasses of convex functions in the unit disc.
Received: 21.07.2006
Citation:
Y. Polatoglu, M. Caglar, A. Sen, “Inequalities for the Schwarzian derivative for subclasses of convex functions in the unit disc”, Vladikavkaz. Mat. Zh., 8:2 (2006), 50–53
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https://www.mathnet.ru/eng/vmj126 https://www.mathnet.ru/eng/vmj/v8/i2/p50
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Abstract page: | 213 | Full-text PDF : | 148 | References: | 45 | First page: | 1 |
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