On Hadamard Type Fractional Inequalities for Riemann–Liouville Integrals via a Generalized Convexity

Abstract

In the literature of mathematical inequalities, convex functions of different kinds are used for the extension of classical Hadamard inequality. Fractional integral versions of the Hadamard inequality are also studied extensively by applying Riemann–Liouville fractional integrals. In this article, we define (α,h−m)-convex function with respect to a strictly monotone function that unifies several types of convexities defined in recent past. We establish fractional integral inequalities for this generalized convexity via Riemann–Liouville fractional integrals. The outcomes of this work contain compact formulas for fractional integral inequalities which generate results for different kinds of convex functions.

Keywords

• Riemann–Liouville integrals
• hadamard inequality
• (<i>α</i>,<i>h</i> − <i>m</i>)-convex function
• convex function