|
This article is cited in 1 scientific paper (total in 1 paper)
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.
Received: 31.08.2018 Revised: 25.10.2018 Accepted: 29.10.2018
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
Linking options:
https://www.mathnet.ru/eng/timm1593 https://www.mathnet.ru/eng/timm/v24/i4/p283
|
Statistics & downloads: |
Abstract page: | 153 | Full-text PDF : | 59 | References: | 33 | First page: | 1 |
|