Mean value theorems for differences
type: Item
instance of: scholarly article
title: Mean value theorems for differences
zbMATH Open document ID: 1172.39030
DOI: 10.4171/EM/97
author: J. M. Ash
published in: Elemente der Mathematik
publication date: 2008-09-08T00:00:00Z
full work available at URL: http://www.ems-ph.org/journals/show_pdf.php
review text: The author offers the folowing mean value theorem. Let \(f: [a,b]\to\mathbb{R}\) be continuous (\(a<b,\;a,b\in\mathbb{R}\)). If there exists an integer \(n\geq 2\) such that (1)\(\;p=(b-a)/n\) then there exists a \(c\in[a-b,p]\) such that (2)\(\;(f(c+p)-f(c))/p=(f(b-a)/(b-a).\) If, however, \(p\) is not of the form (1) then there exists an \(f\in C^{\infty}\) for which (2) does not hold for any \(c\in[a,b-p].\) The rest of the paper contains results for the variants where \([a,b]\) is replaced by the circumference of a circle or by an \(m\)-dimensional interval \((m>1).\)
reviewed by: János Aczél
Mathematics Subject Classification ID: 39B22
Mathematics Subject Classification ID: 26A24
Mathematics Subject Classification ID: 26B05
zbMATH DE Number: 5322348
zbMATH Keywords: mean value theorems
zbMATH Keywords: functional equations
zbMATH Keywords: continuous functions
zbMATH Keywords: \(C^{\infty}\) functions
MaRDI profile type: Publication
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cites work: Q3927416
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description: scientific article; zbMATH DE number 5322348