Properties of Korovkin type in \(L^ p(a,b)\)
type: Item
instance of: scholarly article
title: Properties of Korovkin type in \(L^ p(a,b)\)
zbMATH Open document ID: 0693.41018
DOI: 10.1016/0021-9045(89)90099-3
author: Marie Madeleine Derriennic
published in: Journal of Approximation Theory
publication date: 1989-01-01T00:00:00Z
review text: Let \(\Phi_ i(t)=t^ i\), \(i=0,1,2\). The author shows that a sequence of selfadjoint positive linear operators converges to the identity on \(L^ p(a,b)\), \(p\geq 1\), if and only if it converges for \(\Phi_ 0\) and \(\Phi_ 1\), and the operators are uniformly bounded. Quantitative results in terms of the first modulus of continuity and orders of approximation for the functions \(\Phi_ 0\) and \(\Phi_ 1\) are presented. Furthermore, estimates are given for the order of approximation by a sequence of positive linear, uniformly bounded operators \(L_ n\) in terms of the orders of approximation for \(\Phi_ 0\), \(\Phi_ 1\), \(\Phi_ 2\), and the first modulus of continuity of f.
Mathematics Subject Classification ID: 41A36
Mathematics Subject Classification ID: 41A25
zbMATH DE Number: 4134727
zbMATH Keywords: Korovkin-type property
zbMATH Keywords: selfadjoint positive linear operators
zbMATH Keywords: first modulus of continuity
zbMATH Keywords: orders of approximation
MaRDI profile type: Publication
full work available at URL: 0021-9045(89)90099-3
OpenAlex ID: W2042955388
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description: scientific article; zbMATH DE number 4134727