New Generalized Hermite–Hadamard–Mercer’s Type Inequalities Using (<i>k</i>, <i>ψ</i>)-Proportional Fractional Integral Operator

Abstract

In this paper, by using Jensen–Mercer’s inequality we obtain Hermite–Hadamard–Mercer’s type inequalities for a convex function employing left-sided (k, ψ)-proportional fractional integral operators involving continuous strictly increasing function. Our findings are a generalization of some results that existed in the literature.

Keywords

• convex function
• Jensen–Mercer’s inequality
• Hermite–Hadamard–Mercer’s inequality
• (<i>k</i>, <i>ψ</i>)-proportional fractional integral operator