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ЖУРНАЛЫ // Владикавказский математический журнал // Архив

Владикавк. матем. журн., 2006, том 8, номер 2, страницы 50–53 (Mi vmj126)

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

Аннотация: 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.

УДК: 517.98

Поступила в редакцию: 21.07.2006

Язык публикации: английский



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