Steckin-Marchaud-type inequality of weighted approximation for multivariate Bernstein polynomials (Q2778653)
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scientific article; zbMATH DE number 1721718
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Steckin-Marchaud-type inequality of weighted approximation for multivariate Bernstein polynomials |
scientific article; zbMATH DE number 1721718 |
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2 March 2004
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Stechkin-Marchaud type inequality
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weighted approximation
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multivariate Bernstein polynomials
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Steckin-Marchaud-type inequality of weighted approximation for multivariate Bernstein polynomials (English)
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The authors define some weight functions on the simplex of \({\mathbb R}^d\) first. Then they introduce weight norms and modulus of smoothness relating to these weight functions for the functions defined on the simplex. The result is an inequality of Stechkin-Marchaud type in terms of an introduced weighted modulus for the weighted approximation by multivariate Bernstein polynomials on the simplex.
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