Pointwise approximation by Bernstein polynomials (Q2891964)
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scientific article; zbMATH DE number 6047084
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Pointwise approximation by Bernstein polynomials |
scientific article; zbMATH DE number 6047084 |
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18 June 2012
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Bernstein polynomials
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direct theorems
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Ditzian-Totik moduli of smoothness
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Pointwise approximation by Bernstein polynomials (English)
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The author proves a pointwise estimate for the Bernstein polynomials using the Ditzian-Totik modulus of second order, generalizing in this way an earlier result obtained in 1994 by Ditzian. Next, upper and lower bounds for the function \(g:[0,1]\to \mathbb R,g(x)=x\log(x)+(1-x)\log(1-x), g(0)=g(1)=0\) by Bernstein operators are established.
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