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Sbornik: Mathematics, 2018, Volume 209, Issue 8, Pages 1107–1130
DOI: https://doi.org/10.1070/SM8906 (Mi sm8906) 		 
This article is cited in 11 scientific papers (total in 11 papers)

On the cardinality of the coincidence set for mappings of metric, normed and partially ordered spaces

A. V. Arutyunovabc, E. S. Zhukovskiyd, S. E. Zhukovskiyae

a Peoples Friendship University of Russia, Moscow
b Lomonosov Moscow State University
c Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
d Tambov State University named after G.R. Derzhavin
e Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region
English version PDF (562 kB) Citations (11) Russian version article
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DOI: https://doi.org/10.1070/SM8906
Abstract: Properties of the coincidence set of two mappings are studied. Both single-valued and set-valued mappings are considered. Estimates for the cardinality of the coincidence set are obtained for mappings of metric and partially ordered spaces. For mappings of a normed space to a metric space necessary and sufficient conditions that there exist at least two coincidence points, sufficient conditions that there exist at least $n$ coincidence points, and sufficient conditions that the coincidence set is infinite are given. For abstract inclusions in metric and normed spaces necessary and sufficient conditions that at least one solution exists, sufficient conditions that there exist at least $n$ solutions, and sufficient conditions that the solution set is infinite are put forward. All the results obtained are equally meaningful for set-valued and single-valued mappings.
Bibliography: 21 titles.
Keywords: coincidence point, covering mapping.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 5-100
Russian Science Foundation 17-11-01168
This research was carried out with the financial support of the “5-100” programme of Peoples' Friendship University of Russia. The results of § \ref{s3} and § \ref{s4} were obtained by S. E. Zhukovskiy with the support of the Russian Science Foundation under grant no. 17-11-01168.
Received: 04.01.2017 and 15.01.2018
Bibliographic databases:
Document Type: Article
UDC: 515.126.4
MSC: 54H25, 34A34, 58C06
Language: English
Original paper language: Russian
Citation: A. V. Arutyunov, E. S. Zhukovskiy, S. E. Zhukovskiy, “On the cardinality of the coincidence set for mappings of metric, normed and partially ordered spaces”, Sb. Math., 209:8 (2018), 1107–1130
Citation in format AMSBIB
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\paper On the cardinality of the coincidence set for mappings of metric, normed and partially ordered spaces
\jour Sb. Math.
\yr 2018
\vol 209
\issue 8
\pages 1107--1130
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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