| Pointwise Approximation Theorems for Combinations and Derivatives of Bernstein Polynomials |
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| 作者姓名： | Lin Sen XIE |
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| 作者单位： | Department of Mathematics, Lishui University, Lishui 323000, P. R. China |
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| 基金项目： | The research is supported by Zhejiang Provincial Natural Science Foundation of China |
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| 摘 要： | We establish the pointwise approximation theorems for the combinations of Bernstein polynomials by the rth Ditzian-Totik modulus of smoothness wФ^r（f, t） where Ф is an admissible step-weight function. An equivalence relation between the derivatives of these polynomials and the smoothness of functions is also obtained.
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| 关 键 词： | Bernstein多项式 渐进性 光滑模式 数学分析 |
| 收稿时间： | 2001-10-08 |
| 修稿时间： | 2001-10-082002-03-16 |
Pointwise Approximation Theorems for Combinations
and Derivatives of Bernstein Polynomials |
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| Lin Sen XIE.Pointwise Approximation Theorems for Combinations and Derivatives of Bernstein Polynomials[J].Acta Mathematica Sinica,2005,21(5):1241-1248. |
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| Authors: | Lin Sen Xie |
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| Institution: | (1) Department of Mathematics, Lishui University, Lishui 323000, P. R. China |
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| Abstract: | We establish the pointwise approximation theorems for the combinations of Bernstein polynomials
by the rth Ditzian–Totik modulus of smoothness
where Φ is an admissible step–weight
function. An equivalence relation between the derivatives of these polynomials and the smoothness of
functions is also obtained.
The research is supported by Zhejiang Provincial Natural Science Foundation of China |
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| Keywords: | Bernstein polynomials Combinations and derivatives Ditzian-Totik modulus of smoothness Pointwise approximation |
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