Hermite-Hadamard, Hermite-Hadamard-Fejer, Dragomir-Agarwal and Pachpatte Type Inequalities for Convex Functions via Fractional Integrals

TL;DR

This paper develops new fractional integral inequalities for convex functions, generalizing classical inequalities like Hermite-Hadamard and extending their applicability through exponential kernel operators.

Contribution

It introduces a new class of fractional integral inequalities involving exponential kernels, broadening the scope of convex function inequalities.

Findings

Established Hermite-Hadamard type inequalities for fractional integrals with exponential kernels.

Generalized known inequalities to a broader class of fractional operators.

Provided a foundation for future research in convex analysis and optimization.

Abstract

The aim of this paper is to establish Hermite-Hadamard, Hermite-Hadamard-Fej\'er, Dragomir-Agarwal and Pachpatte type inequalities for new fractional integral operators with exponential kernel. These results allow us to obtain a new class of functional inequalities which generalizes known inequalities involving convex functions. Furthermore, the obtained results may act as a useful source of inspiration for future research in convex analysis and related optimization fields.