Sbornik: Mathematics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






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


Sbornik: Mathematics, 2000, Volume 191, Issue 1, Pages 25–60
DOI: https://doi.org/10.1070/sm2000v191n01ABEH000447
(Mi sm447)
 

This article is cited in 42 scientific papers (total in 43 papers)

$M$-strongly convex subsets and their generating sets

M. V. Balashov, E. S. Polovinkin

Moscow Institute of Physics and Technology
References:
Abstract: For subsets of a Banach space the notions of a generating set $M$ and an $M$-strongly convex set are introduced. The latter can be represented as the intersection of sets of the form $M+x$, which are translates of the generating set $M$. A generating set must satisfy a condition that ensures a special support principle, as shown in the paper. Using this support principle a new area of convex analysis is constructed enabling one to strengthen classical results of the type of the Caratheodory and Krein–Milman theorems. Various classes of generating sets are described and the properties of $M$-strongly convex sets are studied.
Received: 18.02.1999
Russian version:
Matematicheskii Sbornik, 2000, Volume 191, Number 1, Pages 27–64
DOI: https://doi.org/10.4213/sm447
Bibliographic databases:
UDC: 517.977
MSC: Primary 90C25, 49J52, 52A07; Secondary 46B20, 46N10
Language: English
Original paper language: Russian
Citation: M. V. Balashov, E. S. Polovinkin, “$M$-strongly convex subsets and their generating sets”, Mat. Sb., 191:1 (2000), 27–64; Sb. Math., 191:1 (2000), 25–60
Citation in format AMSBIB
\Bibitem{BalPol00}
\by M.~V.~Balashov, E.~S.~Polovinkin
\paper $M$-strongly convex subsets and their generating sets
\jour Mat. Sb.
\yr 2000
\vol 191
\issue 1
\pages 27--64
\mathnet{http://mi.mathnet.ru/sm447}
\crossref{https://doi.org/10.4213/sm447}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1753492}
\zmath{https://zbmath.org/?q=an:1004.46014}
\transl
\jour Sb. Math.
\yr 2000
\vol 191
\issue 1
\pages 25--60
\crossref{https://doi.org/10.1070/sm2000v191n01ABEH000447}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000087494000002}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0034341403}
Linking options:
  • https://www.mathnet.ru/eng/sm447
  • https://doi.org/10.1070/sm2000v191n01ABEH000447
  • https://www.mathnet.ru/eng/sm/v191/i1/p27
  • This publication is cited in the following 43 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник - 1992–2005 Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:1005
    Russian version PDF:462
    English version PDF:46
    References:94
    First page:1
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024