Description

• Title:
  Periodic points of multi-valued $\varepsilon $-contractive maps
• Creator:
  Nadler, Sam B.
• Description:
  Let $(X,d)$ be a nonempty metric space, and let $(2^{X},H_{d})$ be the hyperspace of all nonempty compact subsets of $X$ with the Hausdorff metric. Let $F\colon X\rightarrow 2^{X}$ be an $\varepsilon$-contractive map. A general condition is given that guarantees the existence of a periodic point of $F$ (the theorem extends a result of Edelstein to multi-valued maps). The condition holds when $X$ is compact; hence, $F$ has a periodic point when $X$ is compact. It is shown that $F$ has a fixed point (a point $p\in F(p)$) if $X$ is a continuum. Applications to single-valued $\varepsilon$-expansive maps are given.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2003.12.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 22, No 2 (December 2003); 399 - 409;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2003.048/9586
• Subject:
  Continuum;
  contractive map;
  $\varepsilon$-contractive map;
  $\varepsilon$-expansive map;
  Hausdorff metric;
  fixed point;
  hyperspace;
  multi-valued map;
  open map;
  periodic point;
  Primary 54C60;
  54H25;
  Secondary 54B20
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2003.048
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other