Local approximation by generalized Baskakov-Durrmeyer operators

被引：2

作者：

Abel, Ulrich

Ivan, Mircea

Li, Zhongkai

机构：

[1] Univ Appl Sci, Fachhsch Giessen Friedberg, D-61169 Friedberg, Germany

[2] Tech Univ Cluj Napoca, Dept Math, Cluj Napoca, Romania

[3] Capital Normal Univ, Dept Math, Beijing, Peoples R China

来源：

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2007年 / 28卷 / 3-4期

基金：

美国国家科学基金会; 中国国家自然科学基金;

关键词：

approximation by positive operators; asymptotic expansion; degree of approximation; rate of convergence; simultaneous approximation;

D O I：

10.1080/01630560701277823

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The paper deals with general, Baskakov-Durrmeyer operators containing several previous definitions as special cases. The main results include the local rate of convergence, which is proved based on a representation of the kernel functions in terms of Jacobi polynomials and the complete asymptotic expansion for the sequence of these operators. In obtaining the expansion for simultaneous approximation, a key step is the use of a combinatorical identity for derivatives with weights.

引用

页码：245 / 264

页数：20

共 27 条

[1] On the asymptotic approximation with bivariate operators of Bleimann, Butzer, and Hahn [J].