A Systematic Review on Hermite-Hadamard Inequality: Theory and Applications

TL;DR

This paper systematically reviews Hermite-Hadamard inequalities, covering theoretical formulations and diverse applications, aiming to clarify complex results for new researchers in mathematics and related fields.

Contribution

It compiles and explains various forms of Hermite-Hadamard inequalities, including those involving convexity, differentiable mappings, and fractional integrals, providing a comprehensive resource.

Findings

Summarizes key Hermite-Hadamard inequalities from literature.

Illustrates inequalities with well-known examples.

Highlights the importance of these inequalities across disciplines.

Abstract

Inequalities play important roles not only in mathematics, but also in other fields, such as economics and engineering. Even though many results are published on Hermite-Hadamard (H-H) type inequalities, new researcher to this fields often found it difficult to understand them. Thus, some important discoverers, such as the formulations of H-H type inequalities via various classes of convexity, through differentiable mappings and for fractional integrals, are presented. Some well-known examples from previous literature are used as illustrations.