| 关于推广的Bernstein多项式的逼近 |
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| 引用本文： | 马雪峰,薛银川.关于推广的Bernstein多项式的逼近[J].宝鸡文理学院学报(自然科学版),2006,26(3):176-179. |
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| 作者姓名： | 马雪峰 薛银川 |
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| 作者单位： | 宁夏大学,数学计算机学院,宁夏,银川,750021;宁夏大学,数学计算机学院,宁夏,银川,750021 |
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| 基金项目： | 宁夏大学校科研和教改项目
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宁夏大学校科研和教改项目 |
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| 摘 要： | 目的分析研究推广的Bernstein多项式对连续函数的逼近。方法运用光滑模和K-泛函的等价性以及Berens-Lorentz引理。结果推广了Bernstein多项式的相应点态和整体的正逆定理。结论由于Bernstein多项式的结果是本文的一种特例,我们可以在此基础上做一些更深入的研究。
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| 关 键 词： | 推广的Bernstein多项式 点态逼近 整体逼近 |
| 文章编号： | 1007-1261（2006）03-0176-04 |
| 收稿时间： | 2005-12-10 |
| 修稿时间： | 2006-04-27 |
On the approximation for generalized Bernstein polynomials |
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| MA Xue-feng,XUE Yin-chuan.On the approximation for generalized Bernstein polynomials[J].Journal of Baoji College of Arts and Science(Natural Science Edition),2006,26(3):176-179. |
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| Authors: | MA Xue-feng XUE Yin-chuan |
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| Abstract: | Aim To analyze the approximation of generalized Bernstein polynomials for continuous functions.Methods The relations between modulus of smoothness and K-functional and the lemma of Berens-Lorentz were used.Results The corresponding direct and inverse theorems of pointwise and global approximation about Bernstein polynomials were generalized.Conclusion Some further studies on this base will been done because the results of Bernstein polynomials is just one case. |
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| Keywords: | generalized Bernstein polynomials pointwise approximation global approximation MSC 2000:41A35 41A36 |
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