Some extremal bounds for subclasses of univalent functions

摘要

In this paper we obtain the sharp lower bound for Ref′(z),z∈U, for functions f that are k-uniformly convex in the unit disk U. Next we consider the problem of finding the minimum of Ref′(z) for functions f that are k-uniformly convex in the disk of radius r. Corresponding results for the class of starlike functions related to the class of k-uniformly convex functions are presented.