Email this article ONE EXAMPLE OF A VECTOR-VALUED METRIC IN THE SPACE OF NONEMPTY CLOSED SUBSETS OF A METRIC SPACE
- Authors: Zhukovskiy E.S.1,2, Panasenko E.A.3
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Affiliations:
- Tambov State University named after G.R. Derzhavin
- Peoples’ Friendship University of Russia
- Tambov State University named after G.R. Derzhavina
- Issue: Vol 21, No 2 (2016)
- Pages: 380-385
- Section: Articles
- URL: https://journals.rcsi.science/2686-9667/article/view/365076
- DOI: https://doi.org/10.20310/1810-0198-2016-21-2-380-385
- ID: 365076
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Abstract
In the space of nonempty closed subsets of a given metric space, we define a vector-valued metric which differs from the known vector generalizations of the Hausdorff metric. The metric proposed appears in the analysis of multi-valued maps with possibly unbounded images. It allows to get more information about distances between elements of the corresponding sets and turns out to be convenient in fixed point theorems for multi-valued maps.
About the authors
Evgeny Semenovich Zhukovskiy
Tambov State University named after G.R. Derzhavin; Peoples’ Friendship University of Russia
Email: zukovskys@mail.ru
Doctor of Physics and Mathematics, Professor, Director of the Research Institute for Mathematics, Physics and Informatics; Doctor of Physics and Mathematics, Professor of the Department of Nonlinear Analysis and Optimization Tambov, the Russian Federation; Moscow, the Russian Federation
Elena Aleksandrovna Panasenko
Tambov State University named after G.R. Derzhavina
Email: panlena_t@mail.ru
Candidate of Physics and Mathematics, Associate Professor of the Functional Analysis Department Tambov, the Russian Federation
References
Kurepa D.R. Tableaux ramies d’ensembles. Espaces pseudo distancies // C. R. Acad. Sci. Paris, 1934. V. 198. P. 1563-1565. Proinov P.D. A unified theory of cone metric spaces and its applications to the fixed point theory // Fixed Point Theory and Applications. 2013. Iss. 103. 51 p. doi: 10.1186/1687-1812-2013-103. Asadi M., Soleimani H., Vaezpour S.M. An Order on Subsets of Cone Metric Spaces and Fixed Points of Set-Valued Contractions // Fixed Point Theory and Applications. 2009. 8 p. doi: 10.1155/2009/723203. Zhukovskiy E.S., Panasenko E.A. On multi-valued maps with images in the space of closed subsets of a metric space // Fixed Point Theory and Applications. 2013. Iss. 10. doi: 10.1186/1687-1812-2013-10. Castaing C., Valadier M. Convex Analysis and Measurable Multifunctions. Berlin-Heidelberg-New York: Springer-Verlag, 1977. 278 pp.
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