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 Mat. Sb., 2018, Volume 209, Number 4, Pages 95–116 (Mi msb8855)

Continuous selections in asymmetric spaces

I. G. Tsar'kov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: In asymmetric seminormed and semimetric spaces, sets admitting a continuous $\varepsilon$-selection for any $\varepsilon>0$ are studied. A characterization of closed subsets of a complete symmetrizable asymmetric seminormed space admitting a continuous $\varepsilon$-selection for all $\varepsilon>0$ is obtained. Sufficient conditions for the existence of continuous selections in seminormed linear spaces and semimetric semilinear spaces are put forward. Applications to generalized rational functions in the asymmetric space of continuous functions and in the semilinear space $\mathbf{L}_h$ of all boundedly compact convex sets with Hausdorff metric are found. A metric-topological fixed point theorem for a stable set-valued mapping in the space $\mathbf{L}_h$ is obtained.
Bibliography: 17 titles.

Keywords: continuous selection, semilinear space, asymmetric spaces, generalized rational function, fixed point.

 Funding Agency Grant Number Russian Foundation for Basic Research 16-01-00295-à This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 16-01-00295-a).

DOI: https://doi.org/10.4213/sm8855

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English version:
Sbornik: Mathematics, 2018, 209:4, 560–579

Bibliographic databases:

UDC: 517.982.256
MSC: Primary 41A65; Secondary 54C60, 54F05, 54H25

Citation: I. G. Tsar'kov, “Continuous selections in asymmetric spaces”, Mat. Sb., 209:4 (2018), 95–116; Sb. Math., 209:4 (2018), 560–579

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/msb8855
• https://doi.org/10.4213/sm8855
• http://mi.mathnet.ru/eng/msb/v209/i4/p95

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. G. Poonguzali, M. Marudai, Ch. Park, “Multivalued fixed point in Banach algebra using continuous selection and its application to differential inclusion”, J. Appl. Anal. Comput., 8:6 (2018), 1747–1757
2. I. G. Tsar'kov, “Weakly monotone sets and continuous selection in asymmetric spaces”, Sb. Math., 210:9 (2019), 1326–1347
3. I. G. Tsar'kov, “Approximative properties of sets and continuous selections”, Sb. Math., 211:8 (2020), 1190–1211
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