Sharp Inequalities between the Best Root-Mean-Square Approximations of Analytic Functions in the Disk and Some Smoothness Characteristics in the Bergman Space

被引：0

作者：

Shabozov, M. Sh. ^{[1
]}

Kadamshoev, N. U. ^{[2
]}

机构：

[1] Tajik State Natl Univ, Dushanbe 734025, Tajikistan

[2] Technol Univ Tajikistan, Dushanbe 734000, Tajikistan

来源：

MATHEMATICAL NOTES | 2021年 / 110卷 / 1-2期

关键词：

sharp inequalities; best joint approximation; smoothness characteristics; exact constants; n-widths; POLYNOMIAL APPROXIMATIONS; FOURIER-SERIES; P LESS; CONSTANT; THEOREM;

D O I：

10.1134/S0001434621070269

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In Jackson-Stechkin type inequalities for the smoothness characteristic Lambda(m) (f), m is an element of N, we find exact constants determined by averaging the norms of finite differences of mth order of a function f is an element of B-2. We solve the problem of best joint approximation for a certain class of functions from B-2((r)), r is an element of Z(+) whose smoothness characteristic Lambda(m) (f) averaged with a given weight is bounded above by the majorant Phi. The exact values of n-widths of some classes of functions are also calculated.

引用

页码：248 / 260

页数：13

共 26 条

[21] Smirnov V. I., 1964, The Constructive Theory of Functions of a Complex Variable
[22] Stechkin S.B., 1951, Izv. Ross. Akad. Nauk Ser. Mat., V15, P219
[23] Storozhenko E.A., 1975, MATH USSR SB, V27, P355, DOI 10.1070/SM1975v027n0
[24] STOROZHENKO EA, 1978, SIBERIAN MATH J+, V19, P630
[25] Tikhomirov V. M, 1976, CERTAIN QUESTIONS AP
[26] Inequalities between best polynomial approximations and some smoothness characteristics in the space L 2 and widths of classes of functions
Vakarchuk, S. B.
Zabutnaya, V. I.
[J]. MATHEMATICAL NOTES, 2016, 99 (1-2) : 222 - 242

← 1 2 3 →