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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2020, Volume 308, Pages 42–49
DOI: https://doi.org/10.4213/tm4075 (Mi tm4075) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Coincidence Points and Generalized Coincidence Points of Two Set-Valued Mappings

A. V. Arutyunovab, E. S. Zhukovskiyc, S. E. Zhukovskiya

a V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, ul. Profsoyuznaya 65, Moscow, 117997 Russia
b Institute for Information Transmission Problems (Kharkevich Institute), Russian Academy of Sciences, Bol'shoi Karetnyi per. 19, str. 1, Moscow, 127051 Russia
c Derzhavin Tambov State University, Internatsional'naya ul. 33, Tambov, 392000 Russia
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DOI: https://doi.org/10.4213/tm4075
Abstract: We consider set-valued mappings acting in metric spaces and show that, under natural general assumptions, the set of coincidence points of two such mappings one of which is covering and the other is Lipschitz continuous is dense in the set of generalized coincidence points of these mappings. We use this result to study the coincidence points and generalized coincidence points of a set-valued covering mapping and a set-valued Lipschitz mapping that depend on a parameter. In particular, we obtain conditions that guarantee the existence of a coincidence point for all values of the parameter under the assumption that a coincidence point exists for one value of the parameter.
Keywords: coincidence point, generalized coincidence point, covering set-valued mapping.
Funding agency Grant number
Russian Foundation for Basic Research 17-51-12064
18-01-00106
19-01-00080
Russian Science Foundation 20-11-20131
This work (except for Propositions 1, 3, and 4) was supported by the Russian Foundation for Basic Research, project nos. 17-51-12064, 18-01-00106, and 19-01-00080. The research summarized in Propositions 1, 3, and 4 was performed by the first author and supported by the Russian Science Foundation under grant 20-11-20131.
Received: December 1, 2019
Revised: December 9, 2019
Accepted: December 17, 2019
English version:
Proceedings of the Steklov Institute of Mathematics, 2020, Volume 308, Pages 35–41
DOI: https://doi.org/10.1134/S0081543820010034
Bibliographic databases:
Document Type: Article
UDC: 517+515.126.4
Language: Russian
Citation: A. V. Arutyunov, E. S. Zhukovskiy, S. E. Zhukovskiy, “Coincidence Points and Generalized Coincidence Points of Two Set-Valued Mappings”, Differential equations and dynamical systems, Collected papers, Trudy Mat. Inst. Steklova, 308, Steklov Math. Inst. RAS, Moscow, 2020, 42–49; Proc. Steklov Inst. Math., 308 (2020), 35–41
Citation in format AMSBIB
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\paper Coincidence Points and Generalized Coincidence Points of Two Set-Valued Mappings
\inbook Differential equations and dynamical systems
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
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\vol 308
\pages 42--49
\publ Steklov Math. Inst. RAS
\publaddr Moscow
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    • This publication is cited in the following 3 articles:
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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