On generalization of midpoint type inequalities with generalized fractional integral operators

Abstract

The Hermite-Hadamard inequality is the first principal result for convex functions defined on a interval of real numbers with a natural geometrical interpretation and a loose number of applications for particular inequalities. In this paper we proposed the Hermite-Hadamard and midpoint type inequalities for functions whose first and second derivatives in absolute value are s-convex through the instrument of generalized fractional integral operator and a considerable amount of results for special means which can naturally be deduced.