Widths of Functional Classes Defined by the Majorants of Generalized Moduli of Smoothness in the Spaces Sp

We obtain exact Jackson-type inequalities in terms of the best approximations and averaged values of the generalized moduli of smoothness in the spaces S p . For classes of periodic functions defined by certain conditions imposed on the average values of the generalized moduli of smoothness, we dete...

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Bibliographic Details
Published in:Ukrainian mathematical journal 2021, Vol.73 (6), p.841-858
Main Authors: Abdullayev, F. G., Serdyuk, A. S., Shidlich, A. L.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Geometry
Mathematics
Mathematics and Statistics
Periodic functions
Smoothness
Statistics
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Summary:We obtain exact Jackson-type inequalities in terms of the best approximations and averaged values of the generalized moduli of smoothness in the spaces S p . For classes of periodic functions defined by certain conditions imposed on the average values of the generalized moduli of smoothness, we determine the exact values of the Kolmogorov, Bernstein, linear, and projective widths in the spaces S p .
ISSN:0041-5995
1573-9376
DOI:10.1007/s11253-021-01963-6