Inequalities of Hadamard's type for Lipschitzian mappings and their applications
type: Item
instance of: scholarly article
title: Inequalities of Hadamard's type for Lipschitzian mappings and their applications
zbMATH Open document ID: 0956.26015
author: N. Delaunay
published in: Journal of Mathematical Analysis and Applications
publication date: 2001-02-16T00:00:00Z
full work available at URL: dck1.pdf
review text: The authors prove the following two inequalities of Hadamard's type: Let \(f:I\subseteq \mathbb{R\rightarrow R}\) be an \(M\)-Lipschitzian mapping on \(I\) and \(a,b\in I\) with \(a < b\). Then we have the inequalities \[ \left|f\left( \frac{a+b}{2}\right) -\frac{1}{b-a}\int_{a}^{b}f(x) dx\right|\leq \frac{M}{4}(b-a) \] and \[ \left|\frac{f(a)+f(b)}{2}- \frac{1} {b-a} \int_{a}^{b}f(x) dx\right|\leq \frac{M}{3}(b-a). \] Some applications for means of two positive numbers are also given.
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 26E60
Mathematics Subject Classification ID: 26A16
zbMATH DE Number: 1471626
zbMATH Keywords: Hadamard's inequality
zbMATH Keywords: \(M\)-Lipschitzian mapping
zbMATH Keywords: means
reviewed by: Gheorghe Toader
MaRDI profile type: Publication
OpenAlex ID: W2025968212
cites work: Q3353292
cites work: Q3976943
cites work: Q3983426
cites work: Two mappings in connection to Hadamard's inequalities
cites work: Q5286123
cites work: Q4854410
cites work: Q4287858
cites work: Q4307199
cites work: Q4843519
cites work: Q4843518
cites work: Some remarks on Hadamard's inequalities for convex functions
cites work: Q4032416
cites work: Q3984180
DOI: 10.1006/JMAA.2000.6769
description: scientific article; zbMATH DE number 1471626