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

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

2011-02-02

arxiv.org/abs/1102.0338v1

Mathematics

Complex Variables

12 pages, 1 figure

Scientific paper

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.

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