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 approximants;Bernstein operator;Positive 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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