Porosity results for sets of strict contractions on geodesic metric spaces
Słowa kluczowe
Banach space, hyperbolic space, metric space, nonexpansive mapping, porous set, set-valued mapping, star-shaped set, strict contractionAbstrakt
We consider a large class of geodesic metric spaces, including Banach spaces, hyperbolic spaces and geodesic $\mathrm{CAT}(\kappa)$-spaces, and investigate the space of nonexpansive mappings on either a convex or a star-shaped subset in these settings. We prove that the strict contractions form a negligible subset of this space in the sense that they form a $\sigma$-porous subset. For certain separable and complete metric spaces we show that a generic nonexpansive mapping has Lipschitz constant one at typical points of its domain. These results contain the case of nonexpansive self-mappings and the case of nonexpansive set-valued mappings as particular cases.Pobrania
Opublikowane
2017-05-21
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1.
BARGETZ, Christian, DYMOND, Michael & REICH, Simeon. Porosity results for sets of strict contractions on geodesic metric spaces. Topological Methods in Nonlinear Analysis [online]. 21 maj 2017, T. 50, nr 1, s. 89–124. [udostępniono 22.7.2024].
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