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Matematicheskie Zametki, 2007, Volume 82, Issue 4, Pages 525–529
DOI: https://doi.org/10.4213/mzm3809
(Mi mzm3809)
 

This article is cited in 3 scientific papers (total in 3 papers)

Approximation of Continuous Set-Valued Maps by Constant Set-Valued Maps with Image Balls

S. I. Dudov, A. B. Konoplev

Saratov State University named after N. G. Chernyshevsky
Full-text PDF (395 kB) Citations (3)
References:
Abstract: It is shown that the problem of the best uniform approximation in the Hausdorff metric of a continuous set-valued map with finite-dimensional compact convex images by constant set-valued maps whose images are balls in some norm can be reduced to a visual geometric problem. The latter consists in constructing a spherical layer of minimal thickness which contains the complement of a compact convex set to a larger compact convex set.
Keywords: set-valued map, approximation of set-valued maps, Hausdorff metric, subdifferential, compact convex set.
Received: 17.11.2006
English version:
Mathematical Notes, 2007, Volume 82, Issue 4, Pages 469–473
DOI: https://doi.org/10.1134/S0001434607090222
Bibliographic databases:
UDC: 519.853
Language: Russian
Citation: S. I. Dudov, A. B. Konoplev, “Approximation of Continuous Set-Valued Maps by Constant Set-Valued Maps with Image Balls”, Mat. Zametki, 82:4 (2007), 525–529; Math. Notes, 82:4 (2007), 469–473
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/mzm3809
  • https://doi.org/10.4213/mzm3809
  • https://www.mathnet.ru/eng/mzm/v82/i4/p525
  • This publication is cited in the following 3 articles:
    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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    References:53
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