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.
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