On the Approximation of Differentiable Functions by Bernstein Polynomials and Kantorovich Polynomials

被引：3

作者：

Telyakovskii, S. A. ^{[1
]}

机构：

[1] Russian Acad Sci, VA Steklov Math Inst, Moscow, Russia

来源：

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS | 2008年 / 260卷 / 01期

基金：

俄罗斯基础研究基金会;

关键词：

STEKLOV Institute; Differentiable Function; Asymptotic Representation; Remainder Term; Bernstein Polynomial;

D O I：

10.1134/S0081543808010197

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

E. V. Voronovskaya and S. N. Bernstein established an asymptotic representation for the deviation of functions from Bernstein polynomials under the condition that the function has an even-order derivative. In the present paper, a similar problem is solved in the case when the function has an odd-order derivative. In addition, analogous representations are obtained for the deviations of functions from Kantorovich polynomials.

引用

页码：279 / 286

页数：8