A fixed-point theorem of Krasnoselskii
type: Item
instance of: scholarly article
title: A fixed-point theorem of Krasnoselskii
zbMATH Open document ID: 1127.47318
DOI: 10.1016/S0893-9659(97)00138-9
published in: Applied Mathematics Letters
publication date: 2005-09-27T00:00:00Z
review text: Krasnosel'skij's fixed-point theorem asks for a convex set \(M\) and a mapping \(Pz=Bz+Az\) such that (i) \(Bx+Ay\in M\) for each \(x,y\in M\), (ii) \(A\) is continuous and compact, (iii) \(B\) is a contraction. Then \(P\) has a fixed point. A careful reading of the proof reveals that (i) need only ask that \(Bx+Ay\in M\) when \(x=Bx+Ay\). The proof also yields a technique for showing that such \(x\) is in \(M\).
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 2208930
zbMATH Keywords: fixed points
zbMATH Keywords: integral equation
zbMATH Keywords: periodic solutions
author: T. A. Burton
MaRDI profile type: Publication
cites work: Some problems of nonlinear analysis
cites work: Q3862642
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cites work: Fixpunktsätze vom Krasnoselski-Typ
cites work: Q5551837
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full work available at URL: s0893-9659(97)00138-9
OpenAlex ID: W1965343298
description: scientific article