Ba空间中的多元加权光滑模与Bernstein Durrmeyer算子

Abstract

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

CLC Number:

46E30

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

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