Fixed point theory for \(k\)-CAR sets
type: Item
instance of: scholarly article
title: Fixed point theory for \(k\)-CAR sets
zbMATH Open document ID: 0968.47023
author: Ravi P. Agarwal
author: Donal O'Regan
published in: Journal of Mathematical Analysis and Applications
publication date: 2000-12-19T00:00:00Z
review text: If \(E\) is a Fréchet space, then a subset \(A\) of \(E\) is said to be \(k\)-CAR if there exists a continuous \(k\)-set contractive retraction from \(\overline{\text{conv}} A\) to \(A\). Fixed point results for upper semicontinuous self-multivalued operators between \(k\)-CAR sets, Leray-Schauder type principles for u.s.c. multifunctions \(F:\overline U\to 2^C\) having nonempty values (where \(C\) is a \(k\)-CAR set and \(U\) is open in \(C\)) and a fixed point theorem of Furi-Pera type for upper semicontinuous multifunctions are the main targets of this paper.
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H04
zbMATH DE Number: 1545032
zbMATH Keywords: \(k\)-CAR
zbMATH Keywords: continuous \(k\)-set contractive retraction
zbMATH Keywords: upper semicontinuous self-multivalued operators
zbMATH Keywords: Leray-Schauder type principles
zbMATH Keywords: fixed point theorem of Furi-Pera type
reviewed by: Adrian Petruşel
MaRDI profile type: Publication
full work available at URL: jmaa.2000.7016
OpenAlex ID: W2011849173
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DOI: 10.1006/JMAA.2000.7016
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description: scientific article; zbMATH DE number 1545032