Funktsional'nyi Analiz i ego Prilozheniya
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Funktsional. Anal. i Prilozhen.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Funktsional'nyi Analiz i ego Prilozheniya, 2005, Volume 39, Issue 1, Pages 1–10
DOI: https://doi.org/10.4213/faa27 (Mi faa27) 		 
This article is cited in 11 scientific papers (total in 11 papers)

The Geometric Structure of Chebyshev Sets in $\ell^\infty(n)$

A. R. Alimov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (219 kB) Citations (11)
References:
PDF
HTML
DOI: https://doi.org/10.4213/faa27
Abstract: A subset $M$ of a normed linear space $X$ is called a Chebyshev set if each $x\in X$ has a unique nearest point in $M$. We characterize Chebyshev sets in $\ell^\infty(n)$ in geometric terms and study the approximative properties of sections of Chebyshev sets, suns, and strict suns in $\ell^\infty(n)$ by coordinate subspaces.
Keywords: Chebyshev set, sun, strict sun, best approximation.
Received: 27.02.2003
English version:
Functional Analysis and Its Applications, 2005, Volume 39, Issue 1, Pages 1–8
DOI: https://doi.org/10.1007/s10688-005-0012-x
Bibliographic databases:
Document Type: Article
UDC: 517.982.256
Language: Russian
Citation: A. R. Alimov, “The Geometric Structure of Chebyshev Sets in $\ell^\infty(n)$”, Funktsional. Anal. i Prilozhen., 39:1 (2005), 1–10; Funct. Anal. Appl., 39:1 (2005), 1–8
Citation in format AMSBIB
\Bibitem{Ali05}
\by A.~R.~Alimov
\paper The Geometric Structure of Chebyshev Sets in $\ell^\infty(n)$
\jour Funktsional. Anal. i Prilozhen.
\yr 2005
\vol 39
\issue 1
\pages 1--10
\mathnet{http://mi.mathnet.ru/faa27}
\crossref{https://doi.org/10.4213/faa27}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2132435}
\zmath{https://zbmath.org/?q=an:1087.41027}
\transl
\jour Funct. Anal. Appl.
\yr 2005
\vol 39
\issue 1
\pages 1--8
\crossref{https://doi.org/10.1007/s10688-005-0012-x}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000229257700001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-18144399282}
Linking options:
  • https://www.mathnet.ru/eng/faa27
  • https://doi.org/10.4213/faa27
  • https://www.mathnet.ru/eng/faa/v39/i1/p1
    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024