SOME GENERALIZED HERMITE-HADAMARD TYPE INEQUALITIES INVOLVING FRACTIONAL INTEGRAL OPERATOR FOR FUNCTIONS WHOSE SECOND DERIVATIVES IN ABSOLUTE VALUE ARE S-CONVEX

Abstract

In this article, a general integral identity for twice differentiable mapping involving fractional integral operators is derived. Secondly by using this identity we obtain some new generalized Hermite-Hadamards type inequalities for functions whose absolute values of second derivatives are s-convex and concave. The main results generalize the existing Hermite-Hadamard type inequalities involving the Riemann-Liouville fractional integral. Also we point out, some results in this study in some special cases such as setting s = 1, lambda = alpha, sigma (0) = 1 and w = 0, more reasonable than those obtained in [8].