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Contribution à la recherche de sélections, de points fixes et d'extensions d'applications multivoques

Author: Youcef Askoura; Christiane Godet-Thobie; Université de Bretagne occidentale.
Publisher: [s.l.] : [s.n.], 2006.
Dissertation: Thèse doctorat : Mathématiques : Brest : 2006.
Edition/Format:   Thesis/dissertation : Thesis/dissertation : FrenchView all editions and formats
Summary:
Dans le premier chapitre, j'ai établi l'existence des sélections continues et approchées pour applications multivoques à images non nécessairement convexes. J'ai utilisé des hypothèses relatives aux propriétés de la convexité classique. Dans le deuxième chapitre, j'ai obtenu des points fixes dans les deux cas suivants : 1) pour applications multivoques à images acycliques définies sur des ensembles
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Genre/Form: Thèses et écrits académiques
Additional Physical Format: Contribution à la recherche de sélections, de points fixes et d'extensions d'applications multivoques / Youcef Askoura
Lille : Atelier national de reproduction des thèses, 2006
Microfiches. (@Lille-Thèses)
(ABES)246935634
Material Type: Thesis/dissertation
Document Type: Book
All Authors / Contributors: Youcef Askoura; Christiane Godet-Thobie; Université de Bretagne occidentale.
OCLC Number: 492701138
Description: 1 vol. (102 p.) ; 30cm.
Responsibility: Youcef Askoura ; sous la direction de Christiane Godet-Thobie.

Abstract:

Dans le premier chapitre, j'ai établi l'existence des sélections continues et approchées pour applications multivoques à images non nécessairement convexes. J'ai utilisé des hypothèses relatives aux propriétés de la convexité classique. Dans le deuxième chapitre, j'ai obtenu des points fixes dans les deux cas suivants : 1) pour applications multivoques à images acycliques définies sur des ensembles contractiles (avec des conditions sur les recouvrements du domaine), 2) pour applications multivoque à images infini-proximales connexes (infty-proximally connected) définies sur des convexes d'espaces vectoriels topologiques possédant la propriété d'approximation simpliciale. Mon troisième chapitre est consacré à une version multivoque du théorème spéctral de Scepin. Mon dernier chapitre est dédié à l'extension d'applications multivoques définies soit sur des fermés d'espaces complètement normaux, soit sur des fermés parfaitement normaux d'espaces normaux. Les applications considérées sont semi-continues supérieurement.

In the first chapter, I established the existence of continuous selections and approximate selections for multi-valued maps without convexity assumptions. I used hypotheses relative to the properties of the classical convexity. In the second chapter, I proved the existence of fixed points in the two cases : 1) for multi-valued maps with acyclic values defined on contractible spaces (with additional conditions on convers of the domain), 2) for multi-valued maps with infty-proximally connected values defned on convex subsets of topological vector spaces satisfying the simplicial approximation property. In my third chapter, I gave a multivalued version of the Scepin' spectral theorem. The aim of my last chapter is the extension of multi-valued maps defined either on closed subsets of completely norma spaces or on closed perfectly normal subsets of normal spaces. The considered multi-valued maps are upper semi-continuous.

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