Hermite-Hadamard and Simpson-like type inequalities for differentiable harmonically convex functions

TL;DR

This paper introduces new inequalities for harmonically convex functions using a novel identity, extending Hermite-Hadamard and Simpson-like inequalities, with applications to special means of real numbers.

Contribution

It derives a new identity for differentiable functions and establishes generalized inequalities for harmonically convex functions, expanding existing mathematical frameworks.

Findings

New inequalities for harmonically convex functions are established.

Applications to special means of real numbers are demonstrated.

The paper extends classical inequalities to a broader class of functions.

Abstract

In this paper, a new identity for differentiable functions is derived. A consequence of the identity is that the author establishes some new general inequalities containing all of the Hermite-Hadamard and Simpson-like type for functions whose derivatives in absolute value at certain power are harmonically convex. Some applications to special means of real numbers are also given.