Pointwise Approximation by Szàsz-Mirakjan Quasi-Interpolants  

Szàsz-Mirakjan算子拟中插式的点态逼近等价定理(英文)

作　　者：郭顺生 张更生 刘丽霞 

机构地区：[1]Department of Mathematics,Hebei Normal University

出　　处：《Journal of Mathematical Research and Exposition》2009年第4期629-638,共10页数学研究与评论（英文版）

基　　金：the National Natural Science Foundation of China (No.10571040);the Doctoral Foundation of Hebei Normal University (No.L2004B04)

摘　　要：Recently some classical operator quasi-interpolants were introduced to obtain much faster convergence. A.T. Diallo investigated some approximation properties of Szasz-Mirakjan Quasi-Interpolants, but he obtained only direct theorem with Ditzian-Totik modulus wφ^2r （f, t）. In this paper, we extend Diallo＇s result and solve completely the characterization on the rate of approximation by the method of quasi-interpolants to functions f ∈ CB[0, ∞） by making use of the unified modulus wφ^2r（f, t） （0≤λ≤ 1）.Recently some classical operator quasi-interpolants were introduced to obtain much faster convergence.A.T.Diallo investigated some approximation properties of Szàsz-Mirakjan Quasi-Interpolants,but he obtained only direct theorem with Ditzian-Totik modulus ω2r(f,t).In this paper,we extend Diallo's result and solve completely the characterization on the rate of approximation by the method of quasi-interpolants to functions f∈CB[0,∞) by making use of the unified modulus ω2rλ(f,t)(0≤λ≤1).

关 键 词：Quasi-interpolants Szasz-Mirakjan operator equivalence theorem Ditzian-Totik modulus unified modulus. 

分 类 号：O174.41[理学—数学] O174.42[理学—基础数学]