Convergence-preserving function sequences and uniform convergence
type: Item
instance of: scholarly article
title: Convergence-preserving function sequences and uniform convergence
zbMATH Open document ID: 0939.40001
author: Enno Kolk
published in: Journal of Mathematical Analysis and Applications
publication date: 2000-07-05T00:00:00Z
review text: Consider a sequence of real-valued functions \(\{f_k, k\geq 1\}\) defined on a closed subset \(S\) of the real line. This sequence is called convergence-preserving on \(S\) if \(\{f_k(t_k), k\geq 1\}\) is convergent for every convergent sequence \(\{t_k\} \subset S\). The main result shows that \(\{f_k\}\) is convergence-preserving on a closed interval \([a,b]\) if and only if the sequence \(\{f_k\}\) converges uniformly on \([a,b]\) to a continuous function.
Mathematics Subject Classification ID: 40A30
Mathematics Subject Classification ID: 26A03
zbMATH DE Number: 1375021
zbMATH Keywords: uniform convergence
zbMATH Keywords: regular sequence of functions
zbMATH Keywords: sequence of real-valued functions
zbMATH Keywords: convergence-preserving
zbMATH Keywords: convergent sequence
reviewed by: R. James Tomkins
MaRDI profile type: Publication
full work available at URL: jmaa.1999.6533
OpenAlex ID: W1979376306
cites work: Q3312652
cites work: Convergence-Preserving Functions
DOI: 10.1006/JMAA.1999.6533
description: scientific article; zbMATH DE number 1375021