Convergence of generalized Bernstein polynomials (Q696877)
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scientific article; zbMATH DE number 1800259
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Convergence of generalized Bernstein polynomials |
scientific article; zbMATH DE number 1800259 |
Statements
Convergence of generalized Bernstein polynomials (English)
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12 September 2002
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Let \(f\in C[0,1]\), \(q\in (0,1)\) and \(B_n(f,q;x)\) be generalized Bernstein polynomials based on \(q\)-integers. These polynomials were introduced by G. M. Phillips in 1997. The authors study convergence properties of the sequence \(\{B_n(f,q;x)\}^\infty_{n=1}\). It is shown that in general these properties are essentially different from those in the classical case \(q=1\).
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\(q\)-binomial coefficients
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convergence
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Bernstein polynomials
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\(q\)-integers
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