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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
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.
Received: December 1, 2019 Revised: December 9, 2019 Accepted: December 17, 2019
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
Linking options:
https://www.mathnet.ru/eng/tm4075https://doi.org/10.4213/tm4075 https://www.mathnet.ru/eng/tm/v308/p42
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