Description

• Title:
  Structure of the fixed-point set of mappings with lipschitzian iterates
• Creator:
  Górnicki, Jarosław
• Description:
  We prove, by asymptotic center techniques and some inequalities in Banach spaces, that if $E$ is $p$-uniformly convex Banach space, $C$ is a nonempty bounded closed convex subset of $E$, and $T\colon C\rightarrow C$ has lipschitzian iterates (with some restrictions), then the set of fixed-points is not only connected but even a retract of $C$. The results presented in this paper improve and extend some results in [J. Górnicki, < i> A remark on fixed point theorems for lipschitzian mappings< /i> , J. Math. Anal. Appl. < b> 183< /b> (1994), 495–508], [J. Górnicki, < i> The methods of Hilbert spaces and structure of the fixed-point set of lipschitzian mapping< /i> , Fixed Point Theory and Applications, Hindawi Publ. Corporation, 2009, Article ID 586487].
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2010.04.23
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 36, No 2 (December 2010); 381 - 393;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2010.041/8461
• Subject:
  Retraction;
  asymptotic center;
  fixed point;
  uniformly convex Banach space;
  strongly ergodic matrix;
  Primary 47H09;
  47H10;
  Secondary 54C15
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2010.041
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other