descriptionPublicationkeyboard_double_arrow_right Article 31 Mar 2015Publisher:Steklov Mathematical InstituteJournal:Sbornik: Mathematics, volume 206, pages 370-388 (issn: 1064-5616, eissn: 1468-4802,

Authors: Arutyunov A.V.; Gel'man B.D.;

doi: 10.1070/sm2015v206n03abeh004462

On the structure of the set of coincidence points

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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. © 2015 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd.

Related Organizations

Peoples' Friendship University of Russia
Russian Federation
Voronezh State University
Russian Federation

Keywords

Covering map, Set-valued map, Hausdorff metric, Coincidence point, 510

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