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 (alpha x + (1-alpha)y) <= h(alpha) f (x) + h (1-alpha) f (y), where h is a non-negative function, a E (0, 1) and x, y epsilon J. Some properties of h-convex functions are discussed. Also, the Schur-type inequality is given. (c) 2006 Elsevier Inc. All rights reserved.