Description

• Title:
  On the existence of fixed points for typical nonexpansive mappings on spaces with positive curvature
• Creator:
  Bargetz, Christian;
  Dymond, Michael;
  Medjic, Emir;
  Reich, Simeon
• Description:
  We show that the typical nonexpansive mapping on a small enough subset of a $\CAT(\kappa)$-space is a \textit{contraction in the sense of Rakotch}. By typical we mean that the set of nonexpansive mapppings without this property is a $\sigma$-porous set and therefore also of the first Baire category. Moreover, we exhibit metric spaces where strict contractions are not dense in the space of nonexpansive mappings. In some of these cases we show that all continuous self-mappings have a fixed point nevertheless.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2020 Topological Methods in Nonlinear Analysis
• Date:
  2020.11.27
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 57, No 2 (June 2021); 621 - 634;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2020.040/27128 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2020.040/27129
• Subject:
  Nonexpansive mappings;
  Rakotch contractions;
  spaces of positive curvature;
  $\sigma$-porous sets;
  47H09;
  54E52
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2020.040
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other