Old and new on the Hermite-Hadamard inequality
type: Item
instance of: scholarly article
title: Old and new on the Hermite-Hadamard inequality
zbMATH Open document ID: 1073.26015
author: Constantin P. Niculescu
author: Lars-Erik Persson
published in: Real Analysis Exchange
publication date: 2005-04-04T00:00:00Z
review text: This paper is a survey of the results grown up from the Hermite-Hadamard inequality. Both, old and new results are presented, complemented and discussed within this framework. The Hermite-Hadamard inequality is presented in connection with subdifferentials and quadrature formulae; some improvements of it are discussed. Then a short account on classical Choquet theory is given; a generalization of it is presented, in the same spirit in which the Jensen-Steffensen inequality generalizes the Jensen inequality. A number of problems involving \(n\)-convex functions are discussed. This provides a framework to bring together many nice results, to compare, relate and extend them.
reviewed by: Ioan Raşa
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 41A55
Mathematics Subject Classification ID: 26A51
Mathematics Subject Classification ID: 49J52
zbMATH DE Number: 2151935
zbMATH Keywords: Hermite-Hadamard inequality
zbMATH Keywords: Choquet theory
zbMATH Keywords: subdifferentials
zbMATH Keywords: quadrature
MaRDI profile type: Publication
full work available at URL: realanalexch.29.2.0663
OpenAlex ID: W1531629869
DOI: 10.14321/REALANALEXCH.29.2.0663
description: scientific article; zbMATH DE number 2151935