A family of univariate rational Bernstein operators
A new family of positive rational Bernstein operators of the form \[ R_n(f;\,x)=P_n(f;\,x)/Q_{n-1}(f;\,x)\,,\;\;f\in \mathbb C\;([0,\;1])\,, \] is studied. It is proven that it possesses linear precision, shape preserving and total variation diminishing property. Formulas for the first and second derivatives are carried out. Some convergence results, error estimations and Voronovskaja-type theorems are also given.
scientific article; zbMATH DE number 5641722
scientific article