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

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. © 2018 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd.

Publisher
Russian Academy of Sciences
Number of issue
8
Language
English
Pages
1107-1130
Status
Published
Volume
209
Year
2018
Organizations
  • 1 RUDN University, Moscow, Moscow State University, Institute for Information Transmission Problems of the Russian Academy of Sciences, Russian Federation
  • 2 Tambov State University, Russian Federation
  • 3 RUDN University, Moscow, Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region, Russian Federation
Keywords
Coincidence point; Covering mapping
Date of creation
04.02.2019
Date of change
04.02.2019
Short link
https://repository.rudn.ru/en/records/article/record/36339/
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