Convergence of rational Bernstein operators

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Title: Convergence of rational Bernstein operators
Authors: Render, Hermann
Permanent link: http://hdl.handle.net/10197/5478
Date: 1-Apr-2014
Abstract: In this paper we discuss convergence properties and error estimates of rational Bernstein operators introduced by P. Pit¸ul and P. Sablonni`ere. It is shown that the rational Bernstein operators converge to the identity operator if and only if the maximal difference between two consecutive nodes is converging to zero. Further a Voronovskaja theorem is given based on the explicit computation of higher order moments for the rational Bernstein operator
Type of material: Journal Article
Publisher: Elsevier
Copyright (published version): 2014 Elsevier
Keywords: Rational approximantsBernstein operatorPositive operator
DOI: 10.1016/j.amc.2014.01.152
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

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