Selected Topics on Hermite-Hadamard Inequalities and Applications

TLDR

The Hermite–Hadamard inequality is a foundational result for convex functions on real intervals, offering a geometric interpretation and limited applications to specific inequalities. The monograph aims to present basic facts about Hermite–Hadamard inequalities for convex functions and numerous derived results for special means. The work extends Hermite–Hadamard inequalities to other convexity concepts and refines them using properties of various functions, functionals, and sequences. Recent online references are provided.

Abstract

The Hermite-Hadamard double inequality is the first fundamental result for convex functions defined on a interval of real numbers with a natural geometrical interpretation and a loose number of applications for particular inequalities. In this monograph we present the basic facts related to Hermite- Hadamard inequalities for convex functions and a large number of results for special means which can naturally be deduced. Hermite-Hadamard type inequalities for other concepts of convexities are also given. The properties of a number of functions and functionals or sequences of functions which can be associated in order to refine the result are pointed out. Recent references that are available online are mentioned as well.