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Mat. Zametki, 2019, Volume 106, Issue 4, Pages 565–577 (Mi mz12240)  

This article is cited in 1 scientific paper (total in 1 paper)

Multivalued Homotopy on an Ordered Set, Fixed and Coincidence Points of Mappings, and Applications in Game Theory

D. A. Podoprikhin, T. N. Fomenko

Lomonosov Moscow State University

Abstract: The article develops results of the authors' previous papers on the topic. The notion of the homotopy of a multivalued mapping of an ordered set is introduced. We study the problem as to whether the existence of a fixed point (or a coincidence point) is preserved under multivalued homotopies of a multivalued mapping (or a pair of multivalued mappings). An application of some of the authors' previous results on fixed points in game theory is considered.

Keywords: ordered set, multivalued homotopy, fixed point, coincidence point, pair of equilibrium strategies.

DOI: https://doi.org/10.4213/mzm12240

Full text: PDF file (519 kB)
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English version:
Mathematical Notes, 2019, 106:4, 591–601

Bibliographic databases:

UDC: 512.562+515.126.4+519.813.3
Received: 05.11.2018
Revised: 18.02.2019

Citation: D. A. Podoprikhin, T. N. Fomenko, “Multivalued Homotopy on an Ordered Set, Fixed and Coincidence Points of Mappings, and Applications in Game Theory”, Mat. Zametki, 106:4 (2019), 565–577; Math. Notes, 106:4 (2019), 591–601

Citation in format AMSBIB
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\by D.~A.~Podoprikhin, T.~N.~Fomenko
\paper Multivalued Homotopy on an Ordered Set, Fixed and Coincidence Points of Mappings, and Applications in Game Theory
\jour Mat. Zametki
\yr 2019
\vol 106
\issue 4
\pages 565--577
\mathnet{http://mi.mathnet.ru/mz12240}
\crossref{https://doi.org/10.4213/mzm12240}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=4017570}
\elib{https://elibrary.ru/item.asp?id=41699088}
\transl
\jour Math. Notes
\yr 2019
\vol 106
\issue 4
\pages 591--601
\crossref{https://doi.org/10.1134/S000143461909027X}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85074065160}


Linking options:
  • http://mi.mathnet.ru/eng/mz12240
  • https://doi.org/10.4213/mzm12240
  • http://mi.mathnet.ru/eng/mz/v106/i4/p565

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. P. Kombarov, “On Paranormality in Hyperspaces”, Math. Notes, 109:5 (2021), 832–835  mathnet  crossref  crossref  isi  elib
  • Математические заметки Mathematical Notes
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