Generalized Hermite--Hadamard's inequality for functions convex on the coordinates

TL;DR

This paper extends the Hermite--Hadamard inequality to functions convex on the coordinates, providing a broader framework and new inequalities, including for positive convex functions, enriching the mathematical literature.

Contribution

It generalizes existing inequalities for coordinate-convex functions and introduces a new result for positive functions convex on the coordinates.

Findings

Generalized Hermite--Hadamard inequality for coordinate-convex functions

Derived new inequalities by varying parameter n

Introduced a novel inequality for positive coordinate-convex functions

Abstract

The aim of this paper is to generalize the Hermite--Hadamard inequality for functions convex on the coordinates. Our composite result generalizes the result of Dragomir in \cite{Drag}. Many other interesting inequalities can be derived from our results by choosing different values of $n\in\mathbb{N}.$ Furthermore, we add to the literature a new result for positive functions convex on the coordinates.