Some Generalized Fractional Hermite-Hadamard-Type Inequalities for m-Convex Functions

Abstract

Fractional Hermite-Hadamard-type inequalities represent a significant area of study in convex analysis due to their extensive applications in mathematical and applied sciences. These inequalities provide powerful tools for estimating the integral mean of a convex function in terms of its values at the endpoints of a given interval. In this paper, we focus on the development and refinement of fractional Hermite-Hadamardtype inequalities for the class of twice differentiable m-convex functions. Utilizing advanced analytical techniques, such as H¨older’s inequality and the power mean integral inequality, we derive new bounds that generalize existing results in the literature. These findings not only extend classical inequalities to a broader class of convex functions but also provide sharper and more versatile estimations. The presented results are expected to have significant implications in various mathematical domains, including fractional calculus, optimization, and mathematical modeling. This work contributes to the ongoing efforts to generalize and refine integral inequalities by incorporating fractional operators and broader convexity assumptions, offering a deeper understanding of the behavior of m-convex functions under fractional integration.