The Hermite-Hadamard inequality revisited: Some new proofs and applications

Abstract

New proofs of the classical Hermite-Hadamard inequality are presented and several applications are given, including Hadamard-type inequalities for the functions, whose derivatives have inflection points or whose derivatives are convex. Morever, some estimates from below and above for the first moments of functions about the center point $c=(a+b)/2$ are obtained and the reverse Hardy inequality for convex functions $f:[0,\infty )\to (0,\infty )$ is established.

arXiv comment17 pages, 27 references

References in corpus (1)

• A Note on Hadamard Inequalities for the Product of the Convex Functions