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Fundamentalnaya i Prikladnaya Matematika, 2012, Volume 17, Issue 4, Pages 3–12 (Mi fpm1418)  

This article is cited in 9 scientific papers (total in 9 papers)

Separation of convex sets by extreme hyperplanes

A. R. Alimov, V. Yu. Protasov

M. V. Lomonosov Moscow State University
Full-text PDF (140 kB) Citations (9)
References:
Abstract: The problem of separation of convex sets by extreme hyperplanes (functionals) in normed linear spaces is examined. A concept of a bar (a closed set of a special form) is introduced; it is shown that a bar is characterized by the property that any point not lying in it can be separated from it by an extreme hyperplane. In two-dimensional spaces, in spaces with strictly convex dual, and in the space of continuous functions, any two bars are extremely separated. This property is shown to fail in the space of summable functions. A number of examples and generalizations are given.
English version:
Journal of Mathematical Sciences (New York), 2013, Volume 191, Issue 5, Pages 599–604
DOI: https://doi.org/10.1007/s10958-013-1345-2
Bibliographic databases:
Document Type: Article
UDC: 517.982.252
Language: Russian
Citation: A. R. Alimov, V. Yu. Protasov, “Separation of convex sets by extreme hyperplanes”, Fundam. Prikl. Mat., 17:4 (2012), 3–12; J. Math. Sci., 191:5 (2013), 599–604
Citation in format AMSBIB
\Bibitem{AliPro12}
\by A.~R.~Alimov, V.~Yu.~Protasov
\paper Separation of convex sets by extreme hyperplanes
\jour Fundam. Prikl. Mat.
\yr 2012
\vol 17
\issue 4
\pages 3--12
\mathnet{http://mi.mathnet.ru/fpm1418}
\transl
\jour J. Math. Sci.
\yr 2013
\vol 191
\issue 5
\pages 599--604
\crossref{https://doi.org/10.1007/s10958-013-1345-2}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84884983149}
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  • https://www.mathnet.ru/eng/fpm1418
  • https://www.mathnet.ru/eng/fpm/v17/i4/p3
  • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Фундаментальная и прикладная математика
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    References:67
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