Description

• Title:
  Fixed point for mappings of asymptotically nonexpansive type in Lebesgue spaces with variable exponents
• Creator:
  Benavides, Tomas Domínguez
• Description:
  Assume that $(\Omega, \Sigma, \mu)$ is a $\sigma$-finite measure space and $p\colon\Omega\to [1,\infty]$ a variable exponent. In the case of a purely atomic measure, we prove that the w-FPP for mappings of asymptotically nonexpansive type in the Nakano space $\ell^{p(k)}$, where $p(k)$ is a sequence in $[1,\infty]$, is equivalent to several geometric properties of the space, as weak normal structure, the w-FPP for nonexpansive mappings and the impossibility of containing isometrically $L^1([0,1])$. In the case of an arbitrary $\sigma$-finite measure, we prove that this characterization also holds for pointwise eventually nonexpansive mappings. To determine if the w-FPP for nonexpansive mappings and for mappings of asymptotically nonexpansive type are equivalent is a long standing open question \cite{Ki3}. According to our results, this is the case, at least, for pointwise eventually nonexpansive mappings in Lebesgue spaces with variable exponents.
• Object availability:
  free access
• Rights: https://creativecommons.org/licenses/by-nd/4.0 ;
  Prawa autorskie (c) 2024 Tomas Domínguez Benavides
• Date:
  2024.03.10
• 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); 23 - 38;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/49318/37954 ;https://apcz.umk.pl/TMNA/article/view/49318/37955
• Subject:
  Variable Lebesgue spaces;
  fixed point property;
  nonexpansive mappings;
  mappings of asymptotically nonexpansive type;
  modular spaces;
  Primary: 46E30, 47H10, 46B20
• Identifier: https://apcz.umk.pl/TMNA/article/view/49318
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other