This article is cited in 11 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. Shabozov^a, G. A. Yusupov<sup>b

a</sup> 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.

UDC: 517.5

Received: 31.03.2015

DOI: 10.17377/smzh.2016.57.219

 English version: Siberian Mathematical Journal, 2016, 57:2, 369–376

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