This article is cited 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.

UDC: 512.562+515.126.4+519.813.3

Received: 05.11.2018
Revised: 18.02.2019

DOI: 10.4213/mzm12240

 English version: Mathematical Notes, 2019, 106:4, 591–601

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