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| 多元Bernstein算子的导数与函数的光滑性 | |
| 引用本文： | 曹飞龙,杨汝月,徐宗本.多元Bernstein算子的导数与函数的光滑性[J].应用数学学报,2001,24(4):582-589. |
| 作者姓名： | 曹飞龙 杨汝月 徐宗本 |
| 作者单位： | 1. 宁夏大学数学系, 2. 中国计量学院文理学院, 3. 西安交通大学理学院信息与系统科学研究所, |
| 摘 要： | 利用一个新的光滑性度量刻画多元Bernstein算子方向导数的特征，建立Bernstein算子的导数与逼近函数光滑性之间的等价关系。同时，一个关于一元Bernstein算子的相应结果被推广到多元情形。 |
| 关 键 词： | 多元Bernstein算子 导数 光滑模 方向导数 K－泛函 逼近函数 |
DERIVATIVES OF MULTIVARIATE BERNSTEIN OPERATORS AND SMOOTHNESS OF FUNCTION |
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| CAO FEILONC.DERIVATIVES OF MULTIVARIATE BERNSTEIN OPERATORS AND SMOOTHNESS OF FUNCTION[J].Acta Mathematicae Applicatae Sinica,2001,24(4):582-589. | |
| Authors: | CAO FEILONC |
| Abstract: | We characterize the directional derivatives of multidimensional Bernstein opera- tors by using a new measure of smoothness. This task is carried out by means of establishing a equaivalence relation between the asymptotic behaviour of derivatives of Inultidimensional Bernstein operators and the smoothness of the functions they approximate. Also, a known result on univariate Bernstein operators is extended to the multidimensional cases. |
| Keywords: | Multivariate Bernstein operators derivatives Moduli of smoothness |
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