Description

• Title:
  Fixed points of G-monotone mappings in metric and modular spaces
• Creator:
  Quan, Dau Hong;
  Wiśnicki, Andrzej
• Description:
  Let $C$ be a bounded, closed and convex subset of a reflexive metric space with a digraph $G$ such that $G$-intervals along walks are closed and convex. In the main theorem we show that if $T\colon C\rightarrow C$ is a monotone $G$-nonexpansive mapping and there exists $c\in C$ such that $Tc\in [c,\rightarrow )_{G}$, then $T$ has a fixed point provided for each $a\in C$, $[a,a]_{G}$ has the fixed point property for nonexpansive mappings. In particular, it gives an essential generalization of the Dehaish-Khamsi theorem concerning partial orders in complete uniformly convex hyperbolic metric spaces. Some counterparts of this result for modular spaces, and for commutative families of mappings are given too.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2024 Dau Hong Quan, Andrzej Wiśnicki;
  https://creativecommons.org/licenses/by-nd/4.0
• Date:
  2024.03.03
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 63, No 1 (March 2024); 167 - 184;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/49161/37904 ;https://apcz.umk.pl/TMNA/article/view/49161/37905
• Subject:
  Monotone mapping;
  nonexpansive mapping;
  fixed point;
  Primary 47H10;
  Secondary: 46B20, 47J26, 47H09, 54F05
• Identifier: https://apcz.umk.pl/TMNA/article/view/49161
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other