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Izvestiya: Mathematics, 2012, Volume 76, Issue 4, Pages 840–856
DOI: https://doi.org/10.1070/IM2012v076n04ABEH002606 (Mi im7164) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Stability of convex sets and applications

M. E. Shirokov

Steklov Mathematical Institute, Russian Academy of Sciences
English version PDF (333 kB) Citations (2) Russian version article
References:
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DOI: https://doi.org/10.1070/IM2012v076n04ABEH002606
Abstract: We briefly review the results related to the notion of stability of convex sets and consider some of their applications. We prove a corollary of the stability property which enables us to develop an approximation technique for concave functions on a wide class of convex sets. This technique yields necessary and sufficient conditions for the local continuity of concave functions. We describe some examples of their applications.
Keywords: stable convex set, concave function, weak convergence of probability measures, barycentric map.
Funding agency Grant number
Russian Foundation for Basic Research 10-01-00139-a
12-01-00319-а
Russian Academy of Sciences - Federal Agency for Scientific Organizations
Received: 15.02.2011
Bibliographic databases:
Document Type: Article
UDC: 517.982.25
MSC: 46A55, 52A07, 81P16
Language: English
Original paper language: Russian
Citation: M. E. Shirokov, “Stability of convex sets and applications”, Izv. Math., 76:4 (2012), 840–856
Citation in format AMSBIB
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\by M.~E.~Shirokov
\paper Stability of convex sets and applications
\jour Izv. Math.
\yr 2012
\vol 76
\issue 4
\pages 840--856
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Linking options:
  • https://www.mathnet.ru/eng/im7164
  • https://doi.org/10.1070/IM2012v076n04ABEH002606
  • https://www.mathnet.ru/eng/im/v76/i4/p207
    • This publication is cited in the following 2 articles:
    1. Spitkovsky I.M., Weis S., “Signatures of Quantum Phase Transitions From the Boundary of the Numerical Range”, J. Math. Phys., 59:12 (2018), 121901  crossref  mathscinet  zmath  isi
    2. Weis S., “Maximum-Entropy Inference and Inverse Continuity of the Numerical Range”, Rep. Math. Phys., 77:2 (2016), 251–263  crossref  mathscinet  zmath  isi  elib  scopus
    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
    Statistics & downloads:
    Abstract page:771
    Russian version PDF:226
    English version PDF:34
    References:92
    First page:30
     
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