Metric Subregularity of Composition Set-Valued Mappings with Applications to Fixed Point Theory
In this paper we underline the importance of the parametric subregularity property of set-valued mappings, defined with respect to fixed sets. We show that this property appears naturally for some very simple mappings which play an important role in the theory of metric regularity. We prove a result concerning the preservation of metric subregularity at generalized compositions. Then we obtain, in purely metric setting, several fixed point assertions for set-valued mappings in local and global frameworks.
KeywordsGlobal regularity and subregularity Set-valued compositions Fixed point assertions
Mathematics Subject Classification (2010)90C30 49J52 49J53
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