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 α, 0 < α < 1, and for uniformly convex functions.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap101-1-8,
author = {Stanis\l awa Kanas and Toshiyuki Sugawa},
title = {Sharp norm estimate of Schwarzian derivative for a class of convex functions},
journal = {Annales Polonici Mathematici},
volume = {101},
year = {2011},
pages = {75-86},
zbl = {1220.30065},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap101-1-8}
}
Stanisława Kanas; Toshiyuki Sugawa. Sharp norm estimate of Schwarzian derivative for a class of convex functions. Annales Polonici Mathematici, Tome 101 (2011) pp. 75-86. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap101-1-8/