On (α,β,a,b)-convex functions

Házy, Attila (2015) On (α,β,a,b)-convex functions. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. ISSN 0022-247X (Unpublished)

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Abstract

In this paper we investigate the (α,β,a,b)-convex functions which is a common generalization of the usual convexity, the s-convexity in first and second sense, the h-convexity, the Godunova-Levin functions and the P-functions. This notion of convexity was introduced by Maksa and Páles. The main goal of the paper is to prove some regularity and Bernstein-Doetsch type results for (α,β,a,b)-convex functions.

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