Fejér–Hadamard Type Inequalities for (<i>α</i>, <i>h</i>-<i>m</i>)-<i>p</i>-Convex Functions via Extended Generalized Fractional Integrals

Abstract

Integral operators of a fractional order containing the Mittag-Leffler function are important generalizations of classical Riemann–Liouville integrals. The inequalities that are extensively studied for fractional integral operators are the Hadamard type inequalities. The aim of this paper is to find new versions of the Fejér–Hadamard (weighted version of the Hadamard inequality) type inequalities for (α, h-m)-p-convex functions via extended generalized fractional integrals containing Mittag-Leffler functions. These inequalities hold simultaneously for different types of well-known convexities as well as for different kinds of fractional integrals. Hence, the presented results provide more generalized forms of the Hadamard type inequalities as compared to the inequalities that already exist in the literature.

Keywords

• (<i>α</i>, <i>h</i>-<i>m</i>)-<i>p</i>-convex function
• Fejér–Hadamard inequality
• Mittag-Leffler function
• extended generalized fractional integrals