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Metric Subregularity of Composition Set-Valued Mappings with Applications to Fixed Point Theory

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Abstract

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.

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Authors and Affiliations

  1. Faculty of Mathematics, “Alexandru Ioan Cuza” University of Iaşi, Bd. Carol I, nr. 11, 700506, Iaşi, Romania

    Marius Durea

  2. Department of Mathematics and Informatics, “Gheorghe Asachi” Technical University of Iaşi, Bd. Carol I, nr. 11, 700506, Iaşi, Romania

    Radu Strugariu

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  1. Marius Durea
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  2. Radu Strugariu
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Correspondence to Marius Durea.

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Durea, M., Strugariu, R. Metric Subregularity of Composition Set-Valued Mappings with Applications to Fixed Point Theory. Set-Valued Var. Anal 24, 231–251 (2016). https://doi.org/10.1007/s11228-015-0327-6

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  • DOI: https://doi.org/10.1007/s11228-015-0327-6

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