On stability of fixed points for multi-valued mappings with an application
type: Item
instance of: scholarly article
title: On stability of fixed points for multi-valued mappings with an application
zbMATH Open document ID: 1474.49048
DOI: 10.1155/2014/978257
author: Xianqiang Yang
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: This paper studies the stability of fixed points for multi-valued mappings in relation to selections. For multi-valued mappings admitting Michael selections, some examples are given to show that the fixed point mapping of these mappings are neither upper semi-continuous nor almost lower semi-continuous. Though the set of fixed points may be not compact for multi-valued mappings admitting Lipschitz selections, by finding sub-mappings of such mappings, the existence of minimal essential sets of fixed points is proved, and we show that there exists at least an essentially stable fixed point for almost all these mappings. As an application, we deduce an essentially stable result for differential inclusion problems.
Mathematics Subject Classification ID: 49K40
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 7023441
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/978257
OpenAlex ID: W2010845363
Wikidata QID: Q59043261
cites work: Essential and Non Essential Fixed Points
cites work: The essential components of coincident points for weakly inward and outward set-valued mappings
cites work: On existence and essential components of the solution set for the system of vector quasi-equilibrium problems
cites work: Essential equilibria in normal-form games
cites work: Q5806961
cites work: Markov perfect equilibrium. I: Observable actions
cites work: Some results concerning the generic continuity of set-valued mappings
cites work: Generic stability and essential components of generalized KKM points and applications
cites work: On the stability of the solution for multiobjective generalized games with the payoffs perturbed
cites work: The Generic Stability of Fixed Points for Upper Semicontinuous Mappings in Hyperconvex Metric Spaces
cites work: Q5812718
cites work: Essential Sets and Fixed Points
cites work: Q5331764
cites work: Essential equilibria
cites work: Selected Selection Theorems
cites work: Continuous selections. I
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description: scientific article; zbMATH DE number 7023441