A Korovkin-type theorem for sequences of positive linear operators on function spaces
type: Item
instance of: scholarly article
title: A Korovkin-type theorem for sequences of positive linear operators on function spaces
zbMATH Open document ID: 1493.41016
author: Abderra Dorai
published in: Positivity
publication date: 2021-12-02T00:00:00Z
review text: The author present some Korovkin-type theorems for special sequence of linear positive operators. The main result is the following Theorem. Let \(L_\infty\) be a positive linear operator on \(C[0, 1]\) and let \((L_n)_{n\geq 1}\) be a sequence of positive linear operators on \(C[0, 1]\) satisfying the following conditions: (i) \(\lim_{n\to \infty} L_n(e_2) = L_\infty(e_2)\) uniformly on \([0, 1]\); (ii) \(L_n( f ) \leq L_\infty( f )\) (or \(L_n( f ) \geq L_\infty ( f )\)) for every convex function \(f \in C[0, 1]\) and for every \(n \in \mathbb{}\). Then \(\lim_{n\to \infty} L_n( f ) = L_\infty( f )\) for all \(f \in C[0, 1]\). Several applications are given.
Mathematics Subject Classification ID: 41A36
Mathematics Subject Classification ID: 47B65
Mathematics Subject Classification ID: 47B92
zbMATH DE Number: 7437486
zbMATH Keywords: positive linear operators
zbMATH Keywords: Korovkin-type theorem
zbMATH Keywords: iterates of positive linear operators
reviewed by: Jorge Bustamante
MaRDI profile type: Publication
full work available at URL: s11117-021-00861-2
OpenAlex ID: W3195833863
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DOI: 10.1007/S11117-021-00861-2
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description: scientific article; zbMATH DE number 7437486