Random fixed points of 1-set contractive random maps in Fréchet spaces
type: Item
instance of: scholarly article
title: Random fixed points of 1-set contractive random maps in Fréchet spaces
zbMATH Open document ID: 0973.47047
author: L. A. Khan
author: Nazeer Shahzad
published in: Journal of Mathematical Analysis and Applications
publication date: 2001-04-02T00:00:00Z
review text: This article deals with two theorems on fixed point existence for random operator \(f:\Omega \times S\to X\) \((S\) is a nonempty weakly compact convex subset of a separable Fréchet space \(X\), \((\Omega, {\mathcal A})\) a measurable space); \(f\) is either weakly inward or satisfies the Leray-Schauder condition. If \(f\) is a condensing and, for any \(\omega\in \Omega\), \(f (\omega,S)\) is bounded or if \(f\) is 1-set-contractive operator and, for any \(\omega\in \Omega\), \(f(\omega,S)\) is bounded and \(I-f(\omega, \cdot)\) is demiclosed at zero then it has a random fixed point.
Mathematics Subject Classification ID: 47H40
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 60H25
zbMATH DE Number: 1274771
zbMATH Keywords: fixed point existence
zbMATH Keywords: random operator
zbMATH Keywords: separable Fréchet space
zbMATH Keywords: Leray-Schauder condition
zbMATH Keywords: 1-set-contractive
zbMATH Keywords: demiclosed
zbMATH Keywords: random fixed point
reviewed by: Peter P. Zabreĭko
MaRDI profile type: Publication
full work available at URL: jmaa.1998.6142
OpenAlex ID: W2055337302
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DOI: 10.1006/JMAA.1998.6142
description: scientific article; zbMATH DE number 1274771