Hermite-Hadamard Type Inequalities for Functions Whose Derivatives are Strongly {\varphi}-Convex

TL;DR

This paper derives new Hermite-Hadamard type inequalities for functions with derivatives that are strongly { ext{ extphi}}-convex, expanding the scope of convexity-based inequalities in mathematical analysis.

Contribution

It introduces novel inequalities for functions with derivatives that are strongly { ext{ extphi}}-convex, generalizing existing Hermite-Hadamard inequalities.

Findings

Established new bounds for functions with strongly { ext{ extphi}}-convex derivatives.

Extended Hermite-Hadamard inequalities to a broader class of functions.

Provided theoretical proofs for the derived inequalities.

Abstract

In this paper several inequalities of the right-hand side of Hermite-Hadamard's inequality are obtained for the class of functions whose derivatives in absolutely value at certain powers are strongly {\varphi}-convex with modulus c>0.