Convergence of rational Bernstein operators
Abstract
In this paper we discuss convergence properties and error estimates of rational Bernstein operators introduced by P. Piţul and P. Sablonnière. It is shown that the rational Bernstein operators Rn converge to the identity operator if and only if Δn, the maximal difference between two consecutive nodes of Rn, is converging to zero. Error estimates in terms of Δn are provided. Moreover a Voronovskaja theorem is presented which is based on the explicit computation of higher order moments for the rational Bernstein operator.
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