Description

• Title:
  An extension of Krasnoselskii's fixed point theorem for contractions and compact mappings
• Creator:
  Karakostas, George L.
• Description:
  Let $X$ be a Banach space, $Y$ a metric space, $A\subseteq X$, $C\colon A\to Y$ a compact operator and $T$ an operator defined at least on the set $A\times C(A)$ with values in $X$. By assuming that the family $\{T(\cdot,y):y\in C(A)\}$ is equicontractive we present two fixed point theorems for the operator of the form $Ex:=T(x,C(x))$. Our results extend the well known Krasnosel'skiĭ's fixed point theorem for contractions and compact mappings. The results are used to prove the existence of (global) solutions of integral and integrodifferential equations.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2003.09.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 22, No 1 (September 2003); 181 - 191;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2003.035/9597
• Subject:
  Banach space;
  equicontractions;
  fixed point theorem;
  47H10
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2003.035
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other