Inequalities for the Schwarzian derivative for subclasses of convex functions in the unit disc

Polatoglu Y. , Caglar M. , Sen A.
Владикавказский математический журнал. . Том 8. 2006 г.. Выпуск 2.

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.

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