On Hermite Hadamard-type inequalities for strongly {\varphi}-convex functions

TL;DR

This paper introduces strongly { ext{ extphi}}-convex functions, explores their properties, characterizes inner product spaces using these functions, and establishes Hermite-Hadamard-type inequalities for them.

Contribution

It presents the concept of strongly { ext{ extphi}}-convex functions, provides their properties, and derives new Hermite-Hadamard inequalities for this class.

Findings

Characterization of inner product spaces using strongly { ext{ extphi}}-convex functions

Properties and representations of strongly { ext{ extphi}}-convex functions

Hermite-Hadamard-type inequalities for strongly { ext{ extphi}}-convex functions

Abstract

In this paper, we introduce the notion of strongly {\varphi}-convex functions with respect to c>0 and present some properties and representation of such functions. We obtain a characterization of inner product spaces involving the notion of strongly {\varphi}-convex functions. Finaly, a version of Hermite Hadamard-type inequalities for strongly {\varphi}-convex functions are established.