New Hermite-Hadamard type integral inequalities for convex functions and theirs applications

Abstract

In this paper, we establish (presumably new type) integral inequalities for convex functions via the Hermite--Hadamard's inequalities. As applications, we apply these new inequalities to construct inequalities involving special means of real numbers, some error estimates for the formula midpoint are given. Finally, new inequalities for some special and $q-$special functions are also pointed out.