Convergence of rational Bernstein operators

Hermann Render

Applied Mathematics and Computation, 2014, vol. 232, issue C, 1076-1089

Abstract: In this paper we discuss convergence properties and error estimates of rational Bernstein operators introduced by Piţul and Sablonnière. 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.

Keywords: Rational approximants; Bernstein operator; Positive operator (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:232:y:2014:i:c:p:1076-1089

DOI: 10.1016/j.amc.2014.01.152

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