Upper estimates for best mean-square approximations for some classes of bivariate functions by Fourier-Chebyshev sums.

被引：0

作者：

Shabozov, M. Sh ^{[1
]}

Dzhurakhonov, O. A. ^{[2
]}

机构：

[1] Tajik Natl Univ, Acad NAN Tajikistan, Dushanbe 734025, Tajikistan

[2] Tajik Natl Univ, Dept Funct Anal & Differential Equat, Dushanbe 734025, Tajikistan

来源：

TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN | 2020年 / 26卷 / 04期

关键词：

mean-squared approximation; generalized modulus of continuity; Fourier - Tchebychev double series; translated operator; ALGEBRAIC POLYNOMIALS; WIDTHS; WEIGHT;

D O I：

10.21538/0134-4889-2020-26-4-268-278

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In space L-2,L-rho of bivariate functions summable with square on set Q = [-1, 1](2) with weight rho(x, y) = 1/root(1 - x(2))(1 - y(2)) the sharp inequalities of Jackson-Stechkin type in which the best polynomial approximation estimated above by Peetre K-functional were obtained. We also find the exact values of various widths of classes of functions defined by generalized modulus of continuity and K-functionals. Also the exact upper bounds for modules of coefficients of Fourier - Tchebychev on considered classes of functions were calculated.

引用

页码：268 / 278

页数：11

共 26 条

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