Ba空间中的多元加权光滑模与Bernstein Durrmeyer算子

数学物理学报 ›› 2005, Vol. 25 ›› Issue (5): 627-636.

Ba空间中的多元加权光滑模与Bernstein Durrmeyer算子

丁春梅, 曹飞龙

中国计量学院理学院信息与数学科学系

出版日期:2005-10-25 发布日期:2005-10-25
基金资助:
国家自然科学基金(60473034)资助

Multivariate Weighted Modulus of Smoothness and Bernstein-Durrmeyer Operators in B_a Space

DING Chun-Mei, CAO Fei-Long

Online:2005-10-25 Published:2005-10-25
Supported by:
国家自然科学基金(60473034)资助

摘要/Abstract

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.

关键词: B_a空间, 光滑模单纯形, Bernstein-Durrmeyer算子

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.

Key words: B_a space, Modulus of smoothness, Simplex, Bernstein Durrmeyer operators

中图分类号:

46E30

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, 2005, 25(5): 627-636.

DING Chun-Mei, CAO Fei-Long-. Multivariate Weighted Modulus of Smoothness and Bernstein-Durrmeyer Operators in B_a Space[J]. Acta mathematica scientia,Series A, 2005, 25(5): 627-636.

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