[Banach Space Bulletin Board] Abstract of a paper by Christian Bargetz, Michael Dymond and Simeon Reich
This is an announcement for the paper “Porosity Results for Sets of Strict Contractions on Geodesic Metric Spaces” by Christian Bargetz, Michael Dymond and Simeon Reich. Abstract: We consider a large class of geodesic metric spaces, including Banach spaces, hyperbolic spaces and geodesic $CAT(\kappa)$-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 separable 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. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1602.05230
participants (1)
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Bentuo Zheng (bzheng)