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

2006
Çağlar, Mert
Polatoğlu, Yaşar
Şen, Arzu
Abstract

Nehari norm of the Schwarzian derivative of an analytic function is closely related to its univalence. The famous NehariKraus theorem ((3), (4)) and AhlforsW eill theorem (1) are of fundamental importance in this direction. For a non-constant meromorphic function f on D the unite disc, the Schwarzian derivative Sf of f by is holomorphic at z02 D if and only if f is locally univalent at z0. The aim of this paper is to give sharp estimates of the Nehari norm for the subclasses of convex functions in the unit disc.

Keywords
Schwarzian derivative , convex function