Description

• Title:
  Nonexpansive mappings on Hilbert's metric spaces
• Creator:
  Lemmens, Bas
• Description:
  This paper deals with the iterative behavior of nonexpansive mappings on Hilbert's metric spaces $(X,d_X)$. We show that if $(X,d_X)$ is strictly convex and does not contain a hyperbolic plane, then for each nonexpansive mapping, with a fixed point in $X$, all orbits converge to periodic orbits. In addition, we prove that if $X$ is an open $2$-simplex, then the optimal upper bound for the periods of periodic points of nonexpansive mappings on $(X,d_X)$ is $6$. The results have applications in the analysis of nonlinear mappings on cones, and extend work by Nussbaum and others.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2011.04.23
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 38, No 1 (September 2011); 45 - 58;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2011.023/8411
• Subject:
  Nonexpansive mappings;
  Hilbert's metric;
  periodic orbits;
  hyperbolic plane;
  simplices;
  nonlinear mappings on cones;
  Primary 47H09;
  47H07;
  Secondary 54H20
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2011.023
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other