SIMULTANEOUS APPROXIMATION BY A CLASS OF BERNSTEIN-DURRMEYER OPERATORS PRESERVING LINEAR FUNCTIONS

被引：61

作者：

Gonska, Heiner ^{[1
]}

Paltanea, Radu ^{[2
]}

机构：

[1] Univ Duisburg Essen, D-47048 Duisburg, Germany

[2] Transilvania Univ, RO-500036 Brasov, Romania

来源：

CZECHOSLOVAK MATHEMATICAL JOURNAL | 2010年 / 60卷 / 03期

关键词：

positive linear operator; Bernstein-type operator; genuine Bernstein-Durrmeyer operator; simultaneous approximation; degree of approximation; moduli of continuity; THEOREMS;

D O I：

10.1007/s10587-010-0049-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce and study a one-parameter class of positive linear operators constituting a link between the well-known operators of S. N. Bernstein and their genuine Bernstein-Durrmeyer variants. Several limiting cases are considered including one relating our operators to mappings investigated earlier by Mache and Zhou. A recursion formula for the moments is proved and estimates for simultaneous approximation of derivatives are given.

引用

页码：783 / 799

页数：17

共 19 条

[1]

Berens Y., 1991, APPROXIMATION THEORY, P25

[2]

Chen W., 1987, 5 CHIN C APPR THEOR

[3] APPROXIMATION OF INTEGRABLE FUNCTIONS OVER [0,1] BY MODIFIED BERNSTEIN POLYNOMIALS [J].