| Ba空间中的多元加权光滑模与Bernstein Durrmeyer算子 |
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| 引用本文： | 丁春梅,曹飞龙.Ba空间中的多元加权光滑模与Bernstein Durrmeyer算子[J].数学物理学报(A辑),2005,25(5):627-636. |
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| 作者姓名： | 丁春梅 曹飞龙 |
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| 作者单位： | 中国计量学院理学院信息与数学科学系,杭州310018 |
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| 基金项目： | 国家自然科学基金（60473034）资助 |
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| 摘 要： | 该文引进Ba空间多元加权光滑模,推广L^p空间的DitzianTotik模, 证明该模与K泛函的等价性. 作为应用,讨论定义在单纯形上多元Bernstein-Durrmeyer算子与多元加权光滑模之间的关系. 即以多元加权光滑模为尺度, 建立Bernstein-Durrmeyer算子在Ba空间逼近阶的上界与下界估计.
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| 关 键 词： | B_a空间 光滑模单纯形 Bernstein-Durrmeyer算子 |
| 文章编号： | 1003-3998(2005)05-627-10 |
| 收稿时间： | 2003-05-08 |
| 修稿时间： | 2004-08-09 |
Multivariate Weighted Modulus of Smoothness and Bernstein-Durrmeyer Operators in B_a Space |
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| DING Chun-Mei,CAO Fei-Long.Multivariate Weighted Modulus of Smoothness and Bernstein-Durrmeyer Operators in B_a Space[J].Acta Mathematica Scientia,2005,25(5):627-636. |
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| Authors: | DING Chun-Mei CAO Fei-Long |
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| Institution: | Department of Information and Mathematics Sciences, College of Science, China Jiliang University, Hangzhou 310018 |
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| Abstract: | In this paper, the authors introduce a new multivariate weighted modulus of smoothness in B-a space, which generalizes the Ditzian-Totik's modulus in L p space. The equivalence relationship between the modulus and certain K-functional is shown. As an application, the relationship between the multivariate Bernstein-Durrmeyer operators defined on the simplex and the modulus is discussed as well. Namely, with the modulus as a metric, the upper and lower bounds of degree of approximation by the operators are estimated in B-a space. |
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| Keywords: | Ba space Modulus of smoothness Simplex Bernstein-Durrmeyer operators |
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