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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
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
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
Linking options:
https://www.mathnet.ru/eng/mzm3809https://doi.org/10.4213/mzm3809 https://www.mathnet.ru/eng/mzm/v82/i4/p525
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Abstract page: | 421 | Full-text PDF : | 217 | References: | 53 | First page: | 5 |
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