Description

• Title:
  Fixed point theorems for continuous single-valued and upper semicontinuous set-valued mappings in $p$-vector and locally $p$-convex spaces
• Creator:
  Yuan, George X.
• Description:
  The goal of this paper is to establish a general fixed point theorem for compact single-valued continuous mappings in Hausdorff $p$-vector spaces, and a fixed point theorem for upper semicontinuous set-valued mappings in locally $p$-convex spaces for $p\in (0, 1]$. These results not only provide a solution to Schauder conjecture in the affirmative under the setting of $p$-vector spaces for compact single-valued continuous mappings, but also show the existence of fixed points for upper semicontinuous set-valued mappings defined on $s$-convex subsets in Hausdorff locally $p$-convex spaces, which would be fundamental for nonlinear functional analysis, where $s, p \in (0, 1]$.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2024 George X. Yuan;
  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); 209 - 225;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/49149/37880 ;https://apcz.umk.pl/TMNA/article/view/49149/37881
• Subject:
  Nonlinear functional analysis;
  locally $p$-convex space;
  Schauder conjecture;
  fixed point theorem;
  compact mapping;
  $\alpha$-graph-approximation (graph-approximation);
  upper semicontinuous set-valued mappings;
  47H04, 47H10, 46A16, 46A55, 52A07
• Identifier: https://apcz.umk.pl/TMNA/article/view/49149
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other