Sharp norm estimate of Schwarzian derivative for a class of convex functions

Abstract

We establish a sharp norm estimate of the Schwarzian derivative for a function in the classes of convex functions introduced by Ma and Minda [Proceedings of the Conference on Complex Analysis, International Press Inc., 1992, 157-169]. As applications, we give sharp norm estimates for strongly convex functions of order $\alpha ,0<\alpha <1,$ and for uniformly convex functions.

12 pages, 1 figure