On h-convexity

We introduce a class of h-convex functions which generalize convex, s-convex, Godunova–Levin functions and P-functions. Namely, the h-convex function is defined as a non-negative function f : J → R which satisfies f (αx + (1 − α)y) h(α)f (x) + h(1 − α)f (y), where h is a non-negative function, α ∈ (0, 1) and x,y ∈ J . Some properties of h-convex functions are discussed. Also, the Schur-type inequality is given. © 2006 Elsevier Inc. All rights reserved.