Lyusternik-Graves theorem and fixed points

Asen L. Dontchev Hélène Frankowska 1
1 C&O - Equipe combinatoire et optimisation
UPMC - Université Pierre et Marie Curie - Paris 6, CNRS - Centre National de la Recherche Scientifique : FRE3232
Abstract : Abstract: For set-valued mappings $ F$ and $ \Psi$ acting in metric spaces, we present local and global versions of the following general paradigm which has roots in the Lyusternik-Graves theorem and the contraction principle: if $ F$ is metrically regular with constant $ \kappa$ and $ \Psi$ is Aubin (Lipschitz) continuous with constant $ \mu$ such that $ \kappa\mu <1$, then the distance from $ x$ to the set of fixed points of $ F^{-1}\Psi$ is bounded by $ \kappa/(1-\kappa \mu)$ times the infimum distance between $ \Psi(x)$ and $ F(x)$. From this result we derive known Lyusternik-Graves theorems, a recent theorem by Arutyunov, as well as some fixed point theorems.
Type de document :
Article dans une revue
Proceedings of the American Mathematical Society, American Mathematical Society, 2011, 139, pp.521-534. 〈10.1090/S0002-9939-2010-10490-2〉
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Contributeur : Estelle Bouzat <>
Soumis le : lundi 21 novembre 2011 - 14:38:06
Dernière modification le : mercredi 21 mars 2018 - 18:57:28

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Asen L. Dontchev, Hélène Frankowska. Lyusternik-Graves theorem and fixed points. Proceedings of the American Mathematical Society, American Mathematical Society, 2011, 139, pp.521-534. 〈10.1090/S0002-9939-2010-10490-2〉. 〈hal-00643231〉

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