Some characterizations of convex functions☆

Dedicated to the late Respected Professor Sen-Yen Shaw
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Abstract

The main result in this paper is to establish some new characterizations of convex functions, in which we also simplify the proof of the characterizations given by Bessenyei and Páles.

Keywords

Convex
Locally convex
Characterization
Hermite–Fejér’s inequality
Hermite–Hadamard’s inequality

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This research is supported in part by the National Science Council of Taiwan.

Copyright © 2009 Published by Elsevier Ltd.