Kantorovich型Meyer-Knig-Zeller算子的点态逼近定理  

THE POINTWISE APPROXIMATION THEOREMS FOR THE MEYER-KNIG AND ZELLER-KANTOROVICH TYPE OPERATORS

作　　者：齐秋兰[1] 刘娟[1] 

机构地区：[1]河北师范大学数学与信息科学学院,石家庄050016

出　　处：《高等学校计算数学学报》2011年第2期97-108,共12页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金(10571040);河北省自然科学基金;河北师范大学重点基金

摘　　要：1引言1960年Meyer—K6nigW．和ZellerK．Of the positive operators that are used in the literature one of the most challenging is the Meyer-KSnig and Zeller operators. This is due to the fact that it is difficult to handle their moments. In recent years there are many results about their approximation properties and their transformations, and for their Kantorovich-type modification there are only Lp-approximation （1 ≤ p 〈 ∞）. The aim of the present paper is to study the classical positive estimate in terms of the φ-modulus of smoothness, as well as a corresponding converse. As a result, one can get the classical equivalence of α-order φ-pointwise estimate and the α- order decrease of the ω2φ（f, t）-modulus. The equivalence theorem is as follows： for f∈C[0,1], 0〈α〈2, n≥2, thereare ｜｜M^＊nf-f｜｜=0（n^-Ω/2）→←ω2φ（f, t）=O（t^α）,ω（f,t）=O（t^α/2）.

关 键 词：ZELLER算子 MEYER 点态逼近定理 ch型 

分 类 号：O175.41[理学—数学]