Fractional Hermite–Hadamard–Fejer Inequalities for a Convex Function with Respect to an Increasing Function Involving a Positive Weighted Symmetric Function

Abstract

There have been many different definitions of fractional calculus presented in the literature, especially in recent years. These definitions can be classified into groups with similar properties. An important direction of research has involved proving inequalities for fractional integrals of particular types of functions, such as Hermite–Hadamard–Fejer (HHF) inequalities and related results. Here we consider some HHF fractional integral inequalities and related results for a class of fractional operators (namely, the weighted fractional operators), which apply to function of convex type with respect to an increasing function involving a positive weighted symmetric function. We can conclude that all derived inequalities in our study generalize numerous well-known inequalities involving both classical and Riemann–Liouville fractional integral inequalities.

Keywords

• symmetric
• weighted fractional operators
• convex functions
• Hermite–Hadamard–Fejer inequality