An identity for a general class of approximation operators
type: Item
instance of: scholarly article
title: An identity for a general class of approximation operators
zbMATH Open document ID: 1114.41021
author: Ulrich Abel
published in: Journal of Approximation Theory
publication date: 2006-12-07T00:00:00Z
review text: In \textit{K. Jetter} and \textit{J. Stöckler} [Comput. Aided Geom. Des. 20, No. 8--9, 563--577 (2003; Zbl 1069.41501)] is presented an identity for multivariate Bernstein polynomials on simplices, which may be considered a pointwise orthogonality relation. This univariate form is generalized in the present paper in two directions. Firstly, is allowed the derivatives of the Bernstein basis polynomials to depend on different variables. Secondly, is considered a general class of positive linear approximation operators including the Bernstein operator as a special case, and is proved an identity for the basis functions of that general class of positive linear operators. As application is given a representation of a restricted dual basis and is defined a class of quasi-interpolants.
reviewed by: Zoltán Finta
Mathematics Subject Classification ID: 41A60
Mathematics Subject Classification ID: 26A24
Mathematics Subject Classification ID: 41A36
zbMATH DE Number: 5077949
zbMATH Keywords: Bernstein polynomials
zbMATH Keywords: Szász-Mirakyan operators
zbMATH Keywords: Baskakov operators
MaRDI profile type: Publication
full work available at URL: j.jat.2006.03.005
OpenAlex ID: W2056315425
Wikidata QID: Q115600884
cites work: Q3247255
cites work: New polynomial preserving operators on simplices: direct results
cites work: Direct and converse results on weighted simultaneous approximation by the method of operators of Baskakov-Durrmeyer type
cites work: An identity for multivariate Bernstein polynomials
DOI: 10.1016/J.JAT.2006.03.005
description: scientific article; zbMATH DE number 5077949