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Mathematical Notes

, Volume 106, Issue 3–4, pp 591–601 | Cite as

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

  • D. A. PodoprikhinEmail author
  • T. N. FomenkoEmail author
Article
  • 8 Downloads

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 

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Notes

Acknowledgments

The authors are sincerely grateful to Professor P. S. Gevorkyan and Professor V. V. Obukhovsky for valuable advice regarding the subject of this article.

The authors are very grateful to the anonymous referee for carefully reading the manuscript and a number of comments and suggestions that contributed to the improvement of the presentation.

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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityMoscowRussia

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