On (α,β,a,b)-convex functions

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