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Matematicheskie Zametki, 2002, Volume 71, Issue 1, Pages 37–42
DOI: https://doi.org/10.4213/mzm326 (Mi mzm326) 		 
This article is cited in 4 scientific papers (total in 4 papers)

An Analog of the Krein–Mil'man Theorem for Strongly Convex Hulls in Hilbert Space

M. V. Balashov

Moscow Institute of Physics and Technology
Full-text PDF (160 kB) Citations (4)
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DOI: https://doi.org/10.4213/mzm326
Abstract: We prove the following theorem: in Hilbert space a closed bounded set is contained in the strongly convex R-hull of its R-strong extreme points. R-strong extreme points are a subset of the set of extreme points (it may happen that these two sets do not coincide); the strongly convex R-hull of a set contains the closure of the convex hull of the set.
Received: 15.05.2000
English version:
Mathematical Notes, 2002, Volume 71, Issue 1, Pages 34–38
DOI: https://doi.org/10.1023/A:1013970122469
Bibliographic databases:
UDC: 517.977.8
Language: Russian
Citation: M. V. Balashov, “An Analog of the Krein–Mil'man Theorem for Strongly Convex Hulls in Hilbert Space”, Mat. Zametki, 71:1 (2002), 37–42; Math. Notes, 71:1 (2002), 34–38
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm326
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    • This publication is cited in the following 4 articles:
    1. Shenawy S., “Convex and Starshaped Sets in Manifolds Without Conjugate Points”, Int. Electron. J. Geom., 12:2 (2019), 223–228  crossref  mathscinet  isi
    2. Jahn T. Martini H. Richter Ch., “Ball Convex Bodies in Minkowski Spaces”, Pac. J. Math., 289:2 (2017), 287–316  crossref  mathscinet  zmath  isi  scopus  scopus
    3. F. S. Stonyakin, “Sequential analogues of the Lyapunov and Krein–Milman theorems in Fréchet spaces”, Journal of Mathematical Sciences, 225:2 (2017), 322–344  mathnet  crossref
    4. Balashov M.V., “Antidistance and Antiprojection in the Hilbert Space”, J. Convex Anal., 22:2 (2015), 521–536  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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