POINT WISE APPROXIMATION BY BERNSTEIN POLYNOMIALS

被引：8

作者：

Tachev, Gancho ^{[1
]}

机构：

[1] Univ Architecture Civil Engn & Geodesy, Dept Math, BG-1046 Sofia, Bulgaria

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2012年 / 85卷 / 03期

关键词：

Bernstein polynomials; Direct theorems; Ditzian-Totik moduli of smoothness;

D O I：

10.1017/S0004972711002838

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We improve the degree of pointwise approximation of continuous functions f (x) by Bernstein operators, when x is close to the endpoints of [0, 1]. We apply the new estimate to establish upper and lower pointwise estimates for the test function g(x) = x log(x) + (1 - x) log(1 - x). At the end we prove a general statement for pointwise approximation by Bernstein operators.

引用

页码：353 / 358

页数：6

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