On (h, g; m)-Convexity and the Hermite-Hadamard Inequality

A new class of (h, g; m)-convex functions is presented, together with its properties, thus generalizing several varieties of convexity such as (h−m)-convex functions, (s, m)-Godunova-Levin functions or exponentially (s, m)-convex functions. Also, the Hermite-Hadamard inequality for an (h, g; m)convex function is proved and some special results are pointed out. © Heldermann Verlag.