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Sbornik: Mathematics, 2015, Volume 206, Issue 3, Pages 370–388
DOI: https://doi.org/10.1070/SM2015v206n03ABEH004462 (Mi sm8351) 		 
This article is cited in 13 scientific papers (total in 13 papers)

On the structure of the set of coincidence points

A. V. Arutyunova, B. D. Gel'manb

a Peoples Friendship University of Russia, Moscow
b Voronezh State University
English version PDF (484 kB) Citations (13) Russian version article
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DOI: https://doi.org/10.1070/SM2015v206n03ABEH004462
Abstract: We consider the set of coincidence points for two maps between metric spaces. Cardinality, metric and topological properties of the coincidence set are studied. We obtain conditions which guarantee that this set (a) consists of at least two points; (b) consists of at least $n$ points; (c) contains a countable subset; (d) is uncountable. The results are applied to study the structure of the double point set and the fixed point set for multivalued contractions.
Bibliography: 12 titles.
Keywords: set-valued map, coincidence point, Hausdorff metric, covering map.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 1.333.2014/K
Russian Foundation for Basic Research 14-01-00468
This work is part of the scientific project supported by the Ministry of Education and Science of the Russian Federation (project no. 1.333.2014/K), and was also supported by the Russian Foundation for Basic Research (grant no. 14-01-00468).
Received: 02.03.2014
Bibliographic databases:
Document Type: Article
UDC: 517+515.124+515.126
MSC: 54C05, 54C60, 54E40
Language: English
Original paper language: Russian
Citation: A. V. Arutyunov, B. D. Gel'man, “On the structure of the set of coincidence points”, Sb. Math., 206:3 (2015), 370–388
Citation in format AMSBIB
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\vol 206
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\pages 370--388
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  • https://doi.org/10.1070/SM2015v206n03ABEH004462
  • https://www.mathnet.ru/eng/sm/v206/i3/p35
    • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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