Hermite-Hadamard-type inequalities for (g,\Phi_{h})- convex dominated functions

TL;DR

This paper introduces (g,Φ_h)-convex dominated functions and establishes Hermite-Hadamard-type inequalities for them, extending existing inequalities and broadening the scope of convex analysis.

Contribution

It defines a new class of convex dominated functions and generalizes Hermite-Hadamard inequalities for this class, enhancing the theoretical framework.

Findings

Established properties of (g,Φ_h)-convex dominated functions

Derived Hermite-Hadamard-type inequalities for these functions

Generalized previous convex inequality results

Abstract

In this paper, we introduce the notion of (g,\Phi_{h})-convex dominated function and present some properties of them. Finally, we present a version of Hermite-Hadamard-type inequalities for (g,\Phi_{h})-convex dominated functions. Our results generalize the Hermite-Hadamard-type inequalities in [2], [4] and [6].