The direct and inverse theorems of approximation of functions of several variables with bounded P-variation by polynomials in the Haar

被引：0

作者：

Ahazhanov, T. B. ^{[1
]}

Bokaev, N. A. ^{[2
]}

机构：

[1] Eurasian Natl Univ, Astana, Kazakhstan

[2] Eurasian Natl Univ, Phys Math Sci, Astana, Kazakhstan

来源：

BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS | 2011年 / 63卷 / 03期

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D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we introduce the notion of variations of modulus of continuity for functions of two variables of bounded P-variation. Prove direct and inverse approximation theorems for functions of bounded P-variation by polynomials in the Haar in the norm of the space is main goal of this work. Estimates of the best approximation of a variational module of continuity and assessment of variations of module of continuity through the best approximations are established. Our goal is to extend these results to multiple series. With this purpose in this paper we introduce the notion of variational sum of order P.

引用

页码：11 / 17

页数：7