Convergence of rational Bernstein operators
arXiv:1206.4004
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 R_n converge to the identity operator if and only if Δ_n, the maximal difference between two consecutive nodes of R_n, is converging to zero. Error estimates in terms of Δ_n are provided. Moreover a Voronovskaja theorem is presented which is based on the explicit computation of higher order moments for the rational Bernstein operator.