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

Stanislawa Kanas; Toshiyuki Sugawa

doi:10.4064/ap101-1-8

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

Stanislawa Kanas, Toshiyuki Sugawa

INF - Computer and Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

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 α; 0 < α < 1; and for uniformly convex functions.

Original language	English
Pages (from-to)	75-86
Number of pages	12
Journal	Annales Polonici Mathematici
Volume	101
Issue number	1
DOIs	https://doi.org/10.4064/ap101-1-8
Publication status	Published - 2011

Keywords

Quasiconformal extension
Strongly convex function
Uniformly convex function

ASJC Scopus subject areas

Mathematics(all)

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10.4064/ap101-1-8

Cite this

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AU - Sugawa, Toshiyuki

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AB - 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.

KW - Quasiconformal extension

KW - Strongly convex function

KW - Uniformly convex function

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

Abstract

Keywords

ASJC Scopus subject areas

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