New Inequalities of the type of Hadamard's through $s-(\alpha,m)$ co-ordinated convex functions

TL;DR

This paper extends Hermite-Hadamard inequalities to two-variable functions with second derivatives that are $s-(eta,m)$-convex, providing new bounds and inequalities for such classes of functions.

Contribution

It introduces novel Hadamard-type inequalities for functions with second derivatives that are $s-(eta,m)$-convex, broadening the scope of convexity-based inequalities.

Findings

Derived new inequalities for $s-(eta,m)$-convex functions

Extended Hermite-Hadamard inequalities to two variables

Provided bounds for second order partial derivatives

Abstract

This monograph is associated with the renowned Hermite-Hadamard's integral inequality of $2$-variables on the co-ordinates. In this article we established several inequalities of the type of Hadamard's for the mappings whose absolute values of second order partial derivatives are $s-(\alpha,m)$-convex mappings.