Fixed point theorem in subsets of topological vector spaces
type: Item
instance of: scholarly article
title: Fixed point theorem in subsets of topological vector spaces
zbMATH Open document ID: 1071.54021
author: Y. Askoura
author: Christiane Godet-Thobie
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2005-06-23T00:00:00Z
review text: Let \(E\) be a topological vector space and \(X\) a compact convex subset of \(E\) possessing the simplicial approximation property. Then, in their principal result, the authors show that a multivalued map \(T\) on \(X\) has a fixed point whenever the values of \(T\) have some contractible small neighbourhoods. The map considered by the authors is a generalization of Kakutani maps, viz., upper semicontinuous multivalued maps with convex compact values. The convexity assumption in the values of the map \(T\) is reduced by using some ideas from \textit{Charles D. Horvath} [J. Math. Anal. Appl. 156, 341--357 (1991; Zbl 0733.54011)].
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 54C60
zbMATH DE Number: 2182045
zbMATH Keywords: fixed point
zbMATH Keywords: simplicial approximation property
zbMATH Keywords: cotractible space
zbMATH Keywords: topological vector space
zbMATH Keywords: upper semicontinuous multivalued maps
zbMATH Keywords: Kakutani maps
MaRDI profile type: Publication
full work available at URL: j.crma.2005.04.030
OpenAlex ID: W2040087171
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DOI: 10.1016/J.CRMA.2005.04.030
description: scientific article; zbMATH DE number 2182045