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This article is cited in 10 scientific papers (total in 10 papers)
Best approximation methods and widths for some classes of functions in $H_{q,\rho}$, $1\le q\le\infty$, $0<\rho\le1$
M. Sh. Shabozova, G. A. Yusupovb a Juraev Institute of Mathematics, Tajik Academy of Sciences, Dushanbe, Tajikistan
b Tajik National University, Dushanbe, Tajikistan
Abstract:
We compute the exact values of widths for various widths for the classes $W_{q,a}^{(r)}(\Phi,\mu)$, $\mu\ge1$, of analytic functions in the disk belonging to the Hardy space $H_q$, $q\ge1$, whose averaged moduli of continuity of the boundary values of the derivatives with respect to the argument $f_a^{(r)}$, $r\in\mathbb N$, are dominated by a given function $\Phi$. For calculating the linear and Gelfand $n$-widths, we use best linear approximation for these functions.
Keywords:
best linear approximation method, modulus of continuity, Hardy space, majorant, $n$-width.
Received: 31.03.2015
Citation:
M. Sh. Shabozov, G. A. Yusupov, “Best approximation methods and widths for some classes of functions in $H_{q,\rho}$, $1\le q\le\infty$, $0<\rho\le1$”, Sibirsk. Mat. Zh., 57:2 (2016), 469–478; Siberian Math. J., 57:2 (2016), 369–376
Linking options:
https://www.mathnet.ru/eng/smj2758 https://www.mathnet.ru/eng/smj/v57/i2/p469
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Abstract page: | 231 | Full-text PDF : | 74 | References: | 40 | First page: | 4 |
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