Generalized smoothness characteristics in Jackson-type inequalities and widths of classes of functions in L 2

被引：4

作者：

Vakarchuk, S. B. ^{[1
]}

机构：

[1] Alfred Nobel Dnepropetrovsk Univ, Dnepropetrovsk, Ukraine

来源：

MATHEMATICAL NOTES | 2015年 / 98卷 / 3-4期

关键词：

Jackson-type inequality; n-width of a function class; Steklov operator; smoothness characteristic; generalized shift operator tau(h); Minkowski's inequality; majorant; trigonometric polynomial; Rolle's theorem; POLYNOMIAL-APPROXIMATION; STECHKIN TYPE;

D O I：

10.1134/S0001434615090254

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the space L (2), we study a number of smoothness characteristics of functions; our study is based on the use of the generalized shift operator tau (h) . For the case inwhich tau is the Steklov operator S, we obtain exact constants in Jackson-type inequalities for some classes of 2 pi-periodic functions. We also calculate the exact values of the n-widths of function classes defined by the smoothness characteristics under consideration.

引用

页码：572 / 588

页数：17