【摘要】 该文引进Ba空间多元加权光滑模,推广Lp空间的Ditzian-Totik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.更多还原

【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.更多还原