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.
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页码：572 / 588
页数：17
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