Fixed set theory for closed correspondences with applications to self-similarity and games.
type: Item
instance of: scholarly article
title: Fixed set theory for closed correspondences with applications to self-similarity and games.
zbMATH Open document ID: 1068.47065
author: Efe A. Ok
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2004-03-14T00:00:00Z
review text: The author sketches a general fixed set theory for set-valued maps. It is observed that the existence of a fixed point implies the existence of a nonempty fixed set. If the correspondence is closed, then it is guaranteed to possess a minimal and a largest nonempty closed fixed set. The author also provides sufficient conditions for the fixed sets of the terms of a uniformly convergent sequence of closed self-correspondences on a metric space converge to a fixed set of the limit correspondence. Some applications to game theory are also given.
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 47N10
zbMATH DE Number: 2056127
zbMATH Keywords: fixed sets
zbMATH Keywords: closed correspondences
zbMATH Keywords: condensing correspondences
zbMATH Keywords: Nash equilibrium
reviewed by: Qamrul Hasan Ansari
MaRDI profile type: Publication
full work available at URL: j.na.2003.08.001
OpenAlex ID: W2140225460
Wikidata QID: Q55969266
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DOI: 10.1016/J.NA.2003.08.001
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description: scientific article; zbMATH DE number 2056127