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Trudy Inst. Mat. i Mekh. UrO RAN, 2018, Volume 24, Number 4, Pages 283–294 (Mi timm1593)  

Best restricted approximation of smooth function classes

Y. Liua, G. Xub, J. Zhanga

a School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China
b School of Mathematical Sciences, Tianjin Normal University, Tianjin, 300387, China

Abstract: We first discuss the relative Kolmogorov $n$-widths of classes of smooth $2\pi$-periodic functions for which the modulus of continuity of their $r$-th derivatives does not exceed a given modulus of continuity, and then discuss the best restricted approximation of classes of smooth bounded functions defined on the real axis $\mathbb R$ such that the modulus of continuity of their $r$-th derivatives does not exceed a given modulus of continuity by taking the classes of the entire functions of exponential type as approximation tools. Asymptotic results are obtained for these two problems.

Keywords: modulus of continuity, best restricted approximation, average width.

Funding Agency Grant Number
National Natural Science Foundation of China 11471043
11671271
Beijing Natural Science Foundation 1172004
This work was supported by the National Natural Science Foundation of China (Grant No. 11471043, 11671271) and by the Beijing Natural Science Foundation (Grant No. 1172004). Jie Zhang is the corresponding author.


DOI: https://doi.org/10.21538/0134-4889-2018-24-4-283-294

Full text: PDF file (211 kB)
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Bibliographic databases:

MSC: 41A63, 65Y20, 68Q25
Received: 31.08.2018
Revised: 25.10.2018
Accepted:29.10.2018
Language:

Citation: Y. Liu, G. Xu, J. Zhang, “Best restricted approximation of smooth function classes”, Trudy Inst. Mat. i Mekh. UrO RAN, 24, no. 4, 2018, 283–294

Citation in format AMSBIB
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\by Y.~Liu, G.~Xu, J.~Zhang
\paper Best restricted approximation of smooth function classes
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2018
\vol 24
\issue 4
\pages 283--294
\mathnet{http://mi.mathnet.ru/timm1593}
\crossref{https://doi.org/10.21538/0134-4889-2018-24-4-283-294}
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\elib{https://elibrary.ru/item.asp?id=36517717}


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