The Rate of Approximation by Rational Bernstein Functions in Terms of Second Order Moduli of Continuity

摘要

The aim of this note is to study the impact of the weight numbers in two concrete cases on the rate of approximation by rational Bernstein functions. The approximation is measured in terms of second order moduli of continuity. We consider also the case of rational Bernstein curves and the role of the weights to modify the shape of the curves.