The mean value theorem of Flett and divided differences
type: Item
instance of: scholarly article
title: The mean value theorem of Flett and divided differences
zbMATH Open document ID: 1060.26005
author: Ulrich Abel
author: Mircea Ivan
author: Thomas Riedel
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-08-20T00:00:00Z
review text: Flett's mean value theorem reads as follows: If \(f\) is differentiable on \([a,b]\) and \(f'(a)=f'(b)\), then there exists a point \(c\in(a,b)\) such that \[ f(c)-f(a)=f'(c)(c-a).\tag{11} \] After a careful analysis of divided differences on multiple knots, the authors rewrite as \([a,c,c;f]\) \(=0\) and give condensed representations of other Flett type theorems in terms of divided differences. Several new mean value theorems are obtained. One of them is the following: If \(f\) is continuous on \([a,b]\) and possesses derivatives of order \(n\) at \(a\) and \(b\) such that \(f^{(n)}(a)=f^{(n)}(b)\), then there exists \(c\in(a,b)\) such that in any neighborhood of \(c\) there exist equidistant points \(c_0<\dots<c_n,\;c_0<c<c_n\), with \([a,c_0,\dots,c_n;f]=0\).
reviewed by: Ioan Raşa
Mathematics Subject Classification ID: 26A24
zbMATH DE Number: 2093788
zbMATH Keywords: mean value theorems
zbMATH Keywords: divided differences
MaRDI profile type: Publication
full work available at URL: j.jmaa.2003.10.046
OpenAlex ID: W1968066009
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Wikidata QID: Q115600896
DOI: 10.1016/J.JMAA.2003.10.046
description: scientific article; zbMATH DE number 2093788