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.