Approximate Hermite-Hadamard type inequalities for approximately convex functions

TL;DR

This paper develops approximate Hermite-Hadamard inequalities for functions that are nearly convex relative to a Chebyshev system, extending classical convexity inequalities to approximate settings.

Contribution

It introduces new approximate Hermite-Hadamard inequalities for functions approximately convex with respect to Chebyshev systems, broadening the scope of convex analysis.

Findings

Derived bounds for approximately convex functions

Extended Hermite-Hadamard inequalities to approximate convexity

Applicable to functions with Chebyshev system structure

Abstract

In this paper, approximate lower and upper Hermite--Hadamard type inequalities are obtained for functions that are approximately convex with respect to a given Chebyshev system.