Generalized Fractional Integral Inequalities for Some Classes of Symmetrized Convex Functions

Abstract

In this study, firstly, we prove a new identity for symmetrized convex functions via generalized fractional integral operators. Secondly, with the help of these identities, some new Ilermite-Iladamard type inequalities for some classes of sytnmetrized convex function and Wright-quasi-convex functions are obtained. The main results generalize the existing Elermite-Hadamard type inequalities for symmetrized convex functions involving Riemann-Liouville fractional integrals. Finally, some results in this study, in some special cases, such as setting lambda=alpha, sigma(0) = 1 and w = 0, are found to yield the same results as previous works which studied by Dragomir in [3].