A generalization of Bernstein-Kantorovič operators
type: Item
instance of: scholarly article
title: A generalization of Bernstein-Kantorovič operators
zbMATH Open document ID: 0967.41012
author: Ana M. Valle
author: Jesús de la Cal
published in: Journal of Mathematical Analysis and Applications
publication date: 2001-08-30T00:00:00Z
review text: The authors introduce a double sequence \((L_n^{\langle k \rangle}: n\geq 1,k\geq 0)\) of linear polynomial operators which includes, as particular cases, the Bernstein, Kantorovič and Cao operators. For the operators \(L_n^{\langle k\rangle}\) the authors discuss several approximation properties: the convergence properties, the preservation of global smoothness and classes of functions determined by concave moduli of continuity. A remarcable feature of our approach is that if \(f\) is differentiable, the approximation properties of both \(L_n^{\langle k\rangle}f\) and its derivatives can be discussed simultaneously.
Mathematics Subject Classification ID: 41A35
zbMATH DE Number: 1563090
zbMATH Keywords: linear polynomial operators
zbMATH Keywords: approximation properties
reviewed by: Ion Badea
MaRDI profile type: Publication
full work available at URL: jmaa.2000.7119
OpenAlex ID: W2053531053
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DOI: 10.1006/JMAA.2000.7119
description: scientific article; zbMATH DE number 1563090