Hermite-Hadamard type inequalities for harmonically convex functions on the co-ordinates

TL;DR

This paper introduces harmonically convex functions on the co-ordinates and establishes Hermite-Hadamard type inequalities for these functions, expanding the scope of convex analysis and inequality estimations.

Contribution

It defines a new class of harmonically convex functions on the co-ordinates and derives novel Hermite-Hadamard type inequalities for them.

Findings

Established Hermite-Hadamard inequalities for harmonically convex functions on the co-ordinates.

Extended existing inequalities to this new class of functions.

Provided theoretical bounds and estimations for these functions.

Abstract

In recent years, new classes of convex functions have been introduced in order to generalize the results and to obtain new estimations. We also introduce the concept of harmonically convex functions on the co-ordinates. Also, we establish some inequalities of Hermit-Hadamard type as S.S. Dragomir' s results in Theorem 2 and other Hermit-Hadamard type inequalities for these classes of functions.