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This article is cited in 4 scientific papers (total in 4 papers)
On the order of the best approximation in spaces with asymmetric norm and sign-sensitive weight on classes of differentiable functions
A. I. Kozko M. V. Lomonosov Moscow State University
Abstract:
The class of asymmetric norms with sign-sensitive weight contains both the classical norms of the spaces $L_p(\mathbb T)$ and the metrics that generate one-sided approximations. For sign-sensitive weights $\varrho$, $\tilde\varrho$ and an asymmetric monotone
norm $\psi(u,v)$ on the plane, we obtain an upper estimate for the number
$$
E_n(\mathrm{B}\mathrm{W}_{\psi_{\boldsymbol{\varrho},\mathbf{p}}}^r(\mathbb T),L_{\psi_{\tilde{\boldsymbol{\varrho}},\mathbf{q}}}(\mathbb T))=\sup_{f\in\mathrm{B}\mathrm{W}_{\psi_{\boldsymbol{\varrho},\mathbf{p}}}^r(\mathbb T)}\inf_{t\in T_n}\psi_{\tilde{\boldsymbol{\varrho}},\mathbf{q}}(f(\,\cdot\,)-t(\,\cdot\,)).
$$
In some important cases of asymmetric norms with fixed sign-sensitive weights
$\varrho=(\alpha,\beta)$, we find the rate of decrease of this number as $n\to+\infty$ for a fixed $r\in\mathbb N$.
Received: 14.02.2001
Citation:
A. I. Kozko, “On the order of the best approximation in spaces with asymmetric norm and sign-sensitive weight on classes of differentiable functions”, Izv. Math., 66:1 (2002), 103–131
Linking options:
https://www.mathnet.ru/eng/im373https://doi.org/10.1070/IM2002v066n01ABEH000373 https://www.mathnet.ru/eng/im/v66/i1/p103
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