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This article is cited in 7 scientific papers (total in 7 papers)
Weakly monotone sets and continuous selection in asymmetric spaces
I. G. Tsar'kov
Lomonosov Moscow State University, Moscow, Russia
Abstract:
Sets admitting a continuous selection from the set of near best approximations are studied. Applications of the geometric theory of approximation to the existence of continuous selections for the sets of $n$-link piecewise linear functions, $n$-link piecewise polynomial functions and generalizations thereof are also discussed.
Bibliography: 23 titles.
Keywords:
continuous selection, sun, fixed point.
| Funding Agency |
Grant Number |
Russian Foundation for Basic Research  |
19-01-00332-a |
| This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 19-01-00332-a). |
DOI:
https://doi.org/10.4213/sm9107
 Full text:
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English version:
Sbornik: Mathematics, 2019, 210:9, 1326–1347
Bibliographic databases:
    
UDC:
517.982.256
MSC: Primary 41A65; Secondary 47H10
Received: 29.03.2018 and 23.10.2018
Citation:
I. G. Tsar'kov, “Weakly monotone sets and continuous selection in asymmetric spaces”, Mat. Sb., 210:9 (2019), 129–152; Sb. Math., 210:9 (2019), 1326–1347
Citation in format AMSBIB
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Linking options:
http://mi.mathnet.ru/eng/msb9107https://doi.org/10.4213/sm9107 http://mi.mathnet.ru/eng/msb/v210/i9/p129
Citing articles on Google Scholar:
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This publication is cited in the following articles:
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A. R. Alimov, “Solarity of sets in max-approximation problems”, J. Fixed Point Theory Appl., 21:3 (2019), UNSP 76
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A. R. Alimov, “Vypuklost i monotonnaya lineinaya svyaznost mnozhestv s nepreryvnoi metricheskoi proektsiei v trekhmernykh prostranstvakh”, Tr. IMM UrO RAN, 26, no. 2, 2020, 28–46
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A. R. Alimov, “Characterization of Sets with Continuous Metric Projection in the Space $\ell^\infty_n$”, Math. Notes, 108:3 (2020), 309–317
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A. R. Alimov, “Geometric construction of Chebyshev sets and suns in three-dimensional spaces with cylindrical norm”, Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 75:5 (2020), 209–215
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A. R. Alimov, B. B. Bednov, “Monotone path-connectedness of Chebyshev sets in three-dimensional spaces”, Sb. Math., 212:5 (2021), 636–654
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I. G. Tsar'kov, “Uniform Convexity in Nonsymmetric Spaces”, Math. Notes, 110:5 (2021), 773–783
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A. R. Alimov, I. G. Tsar'kov, “Approximatively Compact Sets in Asymmetric Efimov–Stechkin Spaces and Convexity of Almost Suns”, Math. Notes, 110:6 (2021), 947–951
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