关于Szász-Mirakjan型算子的加权逼近  

WEIGHTED APPROXIMATION BY SZSZ-MIRAKJAN TYPE OPERATORS

作　　者：宣培才 

机构地区：[1]浙江绍兴师专

出　　处：《计算数学》1995年第4期427-442,共16页Mathematica Numerica Sinica

基　　金：浙江省自然科学基金资助项目

摘　　要：设S_n(f;x)表示如下的Sz(?)sz-Mirakjan算子:S_n(f;x)=sum from k=0 to ∞ f(k/n)S_(nk)(x),这里S_(nk)(x)=e^(-nx)(nx)~k/k!,x∈[0,∞),f∈C_[0,∞),C_[0,∞),表示在[0,∞)上连续且有界之函数集,1983年在[1]中给出了Sn(f;x)在一致逼近意义下的特征刻划,为讨论L_p逼近,[2]中引进了如下的Sz(?)sz-Mirakjan-Kantorovich算子:In this paper, we first consider the weighted approximation by Szasz-Mirakjan-Durreyer operators with Jacobi weights in LP[0,∞)and give their characterizations of approximation order. Then we show that the Szasz-Mirakjan operators are unbounded with usual weighted norm, and present a new weighted norm. With this new norm, we obtain the direct and inverse theory and characterization for Szasz-Mirakjan operators with Jacobi weights in uniform approximation.

关 键 词：S-M算子 加权逼近 函数逼近 

分 类 号：O241.5[理学—计算数学]