The Hermite-Hadamard inequality in Beckenbach's setting
type: Item
instance of: scholarly article
title: The Hermite-Hadamard inequality in Beckenbach's setting
zbMATH Open document ID: 1184.26018
author: Mihály Bessenyei
published in: Journal of Mathematical Analysis and Applications
publication date: 2010-02-19T00:00:00Z
review text: Classically, convex functions are characterized geometrically by the property that the graph is sitting above the tangent lines. Beckenbach replaced the tangent lines by a 2-parameter family of continuous functions, requiring that any two distinct points of the plane can be interpolated by a unique member of the family. Such a 2-parameter family induces a generalized notion of convexity of real-valued functions. In this article, the classical Hermite-Hadamard inequality for convex functions is generalized to the context of generalized convex functions in the sense of Beckenbach.
reviewed by: Wing-Sum Cheung
Mathematics Subject Classification ID: 26D15
zbMATH DE Number: 5673223
zbMATH Keywords: Hermite-Hadamard inequality
zbMATH Keywords: Beckenbach families
zbMATH Keywords: Markov-Krein theory
MaRDI profile type: Publication
full work available at URL: j.jmaa.2009.11.015
OpenAlex ID: W2008728166
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DOI: 10.1016/J.JMAA.2009.11.015
description: scientific article; zbMATH DE number 5673223