Hadamard Type Inequalities for m-Convex and ({\alpha},m)-Convex Functions via Fractional Integrals

TL;DR

This paper develops new Hadamard-type inequalities for m-convex and ({\alpha},m)-convex functions using fractional integrals, expanding the theoretical framework of convex analysis.

Contribution

It introduces novel inequalities involving fractional integrals for classes of m-convex and ({\alpha},m)-convex functions, extending existing mathematical results.

Findings

Established new Hadamard-type inequalities for m-convex functions

Derived inequalities for ({\alpha},m)-convex functions using fractional calculus

Extended convex analysis with fractional integral techniques

Abstract

In this paper, we established some new Hadamard-type integral inequalities for functions whose derivatives of absolute values are m-convex and ({\alpha},m)-convex functions via Riemann-Liouville fractional integrals.