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.
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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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Russian Text © The Author(s), 2019, published in Matematicheskie Zametki, 2019, Vol. 106, No. 4, pp. 565–577.
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Podoprikhin, D.A., Fomenko, T.N. Multivalued Homotopy on an Ordered Set, Fixed and Coincidence Points of Mappings, and Applications in Game Theory. Math Notes 106, 591–601 (2019). https://doi.org/10.1134/S000143461909027X
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DOI: https://doi.org/10.1134/S000143461909027X