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.