Description

• Title:
  Porosity results for sets of strict contractions on geodesic metric spaces
• Creator:
  Bargetz, Christian;
  Dymond, Michael;
  Reich, Simeon
• Description:
  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.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2017 Topological Methods in Nonlinear Analysis
• Date:
  2017.05.21
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 50, No 1 (September 2017); 89 - 124;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2017.013/12121 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2017.013/12122
• Subject:
  Banach space;
  hyperbolic space;
  metric space;
  nonexpansive mapping;
  porous set;
  set-valued mapping;
  star-shaped set;
  strict contraction;
  47H09;
  47H04;
  54E52
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2017.013
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other