On new inequalities of Hermite-Hadamard type for functions whose fourth derivative absolute values are quasi-convex with applications

TL;DR

This paper introduces new Hermite-Hadamard type inequalities for functions with quasi-convex fourth derivatives, providing new identities and applications to special means, advancing the understanding of inequalities in mathematical analysis.

Contribution

The paper presents novel inequalities and identities for functions with quasi-convex fourth derivatives, extending Hermite-Hadamard inequalities and applying them to special means.

Findings

Established new Hermite-Hadamard inequalities for quasi-convex fourth derivatives

Derived new identities related to these inequalities

Applied results to special means in analysis

Abstract

We establish some new inequalities of Hermite-Hadamard type for functions whose fourth derivatives absolute values are quasi-convex. Further, we give new identity.Using this new identity, we establish similar inequalities for left-hand side of Hermite-Hadamard result.Also, we present applications to special means.