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.

UDC: 517.98

Received: 21.07.2006

Language: English

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