Approximation by Modified Summation Integral Type Operators in the L_p Spaces  

一类修正的和与积分混合型算子的L_p逼近(英文)

作　　者：齐秋兰 郭顺生 李建坤 

机构地区：[1]College of Mathematics and Information Science, Hebei Normal University

出　　处：《Journal of Mathematical Research and Exposition》2009年第6期1069-1081,共13页数学研究与评论（英文版）

基　　金：the National Natural Science Foundation of China (No.10571040)

摘　　要：The generalized summation integral type operators with Beta basis functions are widely studied. At present, the investigations for the properties of these operators are only limited to the functions of bounded variation. Some authors studied the rate of point-wise rate of convergence, asymptotic formula of Voronovskaja type, and some direct results about these type of operators. The present paper considers the direct, inverse and equivalence theorems of modified summation integral type operators in the Lp spaces.The generalized summation integral type operators with Beta basis functions are widely studied. At present, the investigations for the properties of these operators are only limited to the functions of bounded variation. Some authors studied the rate of point-wise rate of convergence, asymptotic formula of Voronovskaja type, and some direct results about these type of operators. The present paper considers the direct, inverse and equivalence theorems of modified summation integral type operators in the Lp spaces.

关 键 词：Beta operators K-FUNCTIONAL moduli of smoothness Riesz-Thorin interpolationtheorem H61der inequality. 

分 类 号：O174.41[理学—数学] TP311.13[理学—基础数学]