Hermite-Hadamard type inequalities for m-convex functions by using a new inequality for dierentiable functions

In this paper, we give some inequalities for dierentiable convex functions which are connected with the Hermite-Hadamard's integral inequality holding for convex functions. Also, we obtain some estimates to the right-hand side of Hermite-Hadamard inequality for functions whose absolute values of fourth derivatives raised to positive real powers are m-convex. Finally, some natural applications to special means of real numbers are given.

Keywords:

Hermite-Hadamard inequalities , functional inequalities , m-convex functions , quasiconvex functions , Holder inequality