Novel results on Hermite-Hadamard kind inequalities for $\eta$-convex functions by means of $(k,r)$-fractional integral operators

TL;DR

This paper introduces new Hermite-Hadamard type inequalities for $\\eta$-convex functions using generalized $(k,r)$-fractional integrals, broadening existing mathematical results with parameter-based generalizations.

Contribution

It presents novel integral inequalities for $\\eta$-convex functions employing $(k,r)$-fractional operators, extending and generalizing prior theorems in the field.

Findings

New Hermite-Hadamard inequalities for $\\eta$-convex functions.

Generalization of existing inequalities via $(k,r)$-fractional integrals.

Parameter choices yield various specialized inequalities.

Abstract

We establish new integral inequalities of Hermite-Hadamard type for the recent class of $\eta$-convex functions. This is done via generalized $(k,r)$-Riemann-Liouville fractional integral operators. Our results generalize some known theorems in the literature. By choosing different values for the parameters $k$ and $r$, one obtains interesting new results.