Set-Valued and Variational Analysis

, Volume 24, Issue 2, pp 231–251 | Cite as

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.


Global regularity and subregularity Set-valued compositions Fixed point assertions 

Mathematics Subject Classification (2010)

90C30 49J52 49J53 


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Faculty of Mathematics“Alexandru Ioan Cuza” University of IaşiIaşiRomania
  2. 2.Department of Mathematics and Informatics“Gheorghe Asachi” Technical University of IaşiIaşiRomania

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