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Izv. RAN. Ser. Mat., 2012, Volume 76, Issue 4, Pages 207–224 (Mi izv7164)  

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

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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


DOI: https://doi.org/10.4213/im7164

Full text: PDF file (596 kB)
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English version:
Izvestiya: Mathematics, 2012, 76:4, 840–856

Bibliographic databases:

UDC: 517.982.25
MSC: 46A55, 52A07, 81P16
Received: 15.02.2011

Citation: M. E. Shirokov, “Stability of convex sets and applications”, Izv. RAN. Ser. Mat., 76:4 (2012), 207–224; Izv. Math., 76:4 (2012), 840–856

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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
    2. 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
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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