Some New Inequalities for (h-s)_{1,2}-convex Functions via Further Properties

TL;DR

This paper introduces new Hermite-Hadamard type inequalities for (h-s)_{1,2}-convex functions, expanding the theoretical framework for these convexity classes and their properties.

Contribution

The paper develops novel inequalities for (h-s)_{1,2}-convex functions, including cases that are ordinary, super-multiplicative, or similarly ordered, broadening existing convexity inequalities.

Findings

Derived new Hermite-Hadamard inequalities for (h-s)_{1,2}-convex functions.

Extended inequalities to functions that are super-multiplicative or similarly ordered.

Provided theoretical properties and conditions for these inequalities.

Abstract

In this paper, we establish some new inequalities of the Hermite-Hadamard like for class of (h-s)_{1,2}-convex functions which are ordinary, super-multiplicative or similarly ordered and nonnegative.