New Hermite-Hadamard Type Inequalities for Convex Mappings Utilizing Generalized Fractional Integrals

Abstract

In this work, we first establish new Hermite-Hadamard inequalities for convex function utilizing fractional integrals with respect to another function which are generalization of some important fractional integrals such as the Riemann-Liouville fractional integrals and the Hadamard fractional integrals. Moreover, we obtain some generalized midpoint and trapezoid type inequalities for these kinds of fractional integrals. The inequalities given in this paper provide generalizations of several results obtained in earlier works.