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

Complex Variables 2011-02-03 v1

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 α, 0<α<1,\alpha,~0<\alpha<1, and for uniformly convex functions.

Keywords

Cite

@article{arxiv.1102.0338,
  title  = {Sharp norm estimate of Schwarzian derivative for a class of convex functions},
  author = {Stanisława Kanas and Toshiyuki Sugawa},
  journal= {arXiv preprint arXiv:1102.0338},
  year   = {2011}
}

Comments

12 pages, 1 figure