Open Access
2014 On Stability of Fixed Points for Multi-Valued Mappings with an Application
Qi-Qing Song
Abstr. Appl. Anal. 2014(SI05): 1-5 (2014). DOI: 10.1155/2014/978257


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.


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Qi-Qing Song. "On Stability of Fixed Points for Multi-Valued Mappings with an Application." Abstr. Appl. Anal. 2014 (SI05) 1 - 5, 2014.


Published: 2014
First available in Project Euclid: 6 October 2014

MathSciNet: MR3176783
Digital Object Identifier: 10.1155/2014/978257

Rights: Copyright © 2014 Hindawi

Vol.2014 • No. SI05 • 2014
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