QUANTITATIVE CONVERGENCE THEOREMS FOR A CLASS OF BERNSTEIN-DURRMEYER OPERATORS PRESERVING LINEAR FUNCTIONS

被引：23

作者：

Gonska, H. ^{[1
]}

Paltanea, R. ^{[2
]}

机构：

[1] Univ Duisburg Essen, Duisburg, Germany

[2] Transilvania Univ, Brasov, Romania

来源：

UKRAINIAN MATHEMATICAL JOURNAL | 2010年 / 62卷 / 07期

关键词：

Uniform Convergence; Bernstein Polynomial; Positive Linear Operator; Bernstein Operator; Durrmeyer Operator;

D O I：

10.1007/s11253-010-0413-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We supplement recent results on a class of Bernstein-Durrmeyer operators preserving linear functions. This is done by discussing two limiting cases and proving quantitative Voronovskaya-type assertions involving the first-order and second-order moduli of smoothness. The results generalize and improve earlier statements for Bernstein and genuine Bernstein-Durrmeyer operators.

引用

页码：1061 / 1072

页数：12