Description

• Title:
  Function and colorful extensions of the KKM theorem
• Creator:
  Kulpa, Władysław;
  Szymański, Andrzej;
  Turzański, Marian
• Description:
  We deal with an aggregate version of the KKM theorem. Given $n$ KKM families of special type on an $( n-1)$-dimensional simplex, we show that it is possible to choose a single element from every KKM family to get a KKM family on that simplex. We also introduce and study function KKM families as surrogates of KKM families on simplexes. We show a function version of the KKM theorem. The Coincidence Theorem is our main result, Brouwer's fixed is a special cases of that theorem.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2020 Topological Methods in Nonlinear Analysis
• Date:
  2020.09.05
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 56, No 1 (September 2020); 313 - 324;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2020.015/26468 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2020.015/26469
• Subject:
  Simplex;
  corner set;
  KKM theorem;
  Primary;
  52C45;
  54F05;
  Secondary;
  52A07;
  55M20
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2020.015
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other