Integral inequalities for s-convexity via generalized fractional integrals on fractal sets

TL;DR

This paper introduces new Hermite-Hadamard type integral inequalities for s-convex functions using generalized fractional integrals, unifying several existing fractional integral forms and applying them to special means.

Contribution

It develops a unified framework for integral inequalities involving s-convexity and generalized fractional integrals on fractal sets, extending previous results.

Findings

Established new Hermite-Hadamard type inequalities for s-convex functions

Unified various fractional integral forms into a single generalized integral

Provided applications to special means using the new inequalities

Abstract

In this study, we establish a new integral inequalities of Hermite-Hadamard type for $s$-convexity via Katugampola fractional integral. This generalizes the Hadamard fractional integrals and Riemann-Liouville into a single form. We show that the new integral inequalities of Hermite-Hadamard type can be obtained via the Riemann-Liouville fractional integral. Finally, we give some applications to special means.