Sharp norm estimate of Schwarzian derivative for a class of convex functions
Volume 101 / 2011
Annales Polonici Mathematici 101 (2011), 75-86
MSC: Primary 30C45; Secondary 30F60.
DOI: 10.4064/ap101-1-8
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, Int. Press, 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.
