Linear operators that preserve some test functions
type: Item
instance of: scholarly article
title: Linear operators that preserve some test functions
zbMATH Open document ID: 1121.41018
DOI: 10.1155/IJMMS/2006/94136
author: Octavian Agratini
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2007-06-14T00:00:00Z
full work available at URL: https://eudml.org/doc/53454
review text: The Korovkin Theorem states that if \(\{L_n\}\) is a sequence of positive operators such that \(L_n(x^i)\) converges to \(x^i\) for \(i=0,1,2\), then \(L_n(f)\) converges to \(f\) for all continuous functions on \([a,b]\). The author constructs positive operators \(L_n\) such that \(L_n(x^i)\) converges to \(x^i\) for \(i=0,2\). He then relates the convergence of \(L_n(f)\) to \(f\) to the rate of convergence of \(L_n(x)\) to \(x\) for various moduli of smoothness of \(f\).
reviewed by: Daniel Wulbert
Mathematics Subject Classification ID: 41A36
zbMATH DE Number: 5164271
MaRDI profile type: Publication
cites work: Korovkin-type approximation theory and its applications
cites work: Q4357786
cites work: Q3878114
cites work: Q4042065
cites work: Q4371330
cites work: Q4724238
cites work: Positive linear operators which preserve \(x^2\)
cites work: Weighted simultaneous approximation with Baskakov type operators
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description: scientific article; zbMATH DE number 5164271