A family of univariate rational Bernstein operators (Q1041617)
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scientific article; zbMATH DE number 5641722
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A family of univariate rational Bernstein operators |
scientific article; zbMATH DE number 5641722 |
Statements
A family of univariate rational Bernstein operators (English)
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3 December 2009
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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.
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positive operators
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rational approximants
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