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Izvestiya: Mathematics, 2002, Volume 66, Issue 1, Pages 103–131
DOI: https://doi.org/10.1070/IM2002v066n01ABEH000373
(Mi im373)
 

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
References:
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
Bibliographic databases:
UDC: 517.518
Language: English
Original paper language: Russian
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
Citation in format AMSBIB
\Bibitem{Koz02}
\by A.~I.~Kozko
\paper On the order of the best approximation in spaces with asymmetric norm and sign-sensitive weight on classes of differentiable functions
\jour Izv. Math.
\yr 2002
\vol 66
\issue 1
\pages 103--131
\mathnet{http://mi.mathnet.ru//eng/im373}
\crossref{https://doi.org/10.1070/IM2002v066n01ABEH000373}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1917539}
\zmath{https://zbmath.org/?q=an:1052.41018}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-12344253686}
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  • https://doi.org/10.1070/IM2002v066n01ABEH000373
  • https://www.mathnet.ru/eng/im/v66/i1/p103
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
     
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