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| HAL : hal-00699225, version 1 |
| Fiche détaillée |  Récupérer au format |
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| Journal of Mathematical Analysis and applications 152, 1 (1990) 46-60 |
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| Fixed points for Kakutani factorizable multifunctions |
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| Marc Lassonde 1 |
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| (1990) |
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| A multifunction Γ is called a Kakutani multifunction if there exist two nonempty convex sets X and Y , each in a Hausdorff topological vector space, such that Γ : X → Y is upper semi-continuous with nonempty compact convex values. We prove the following extension of the Kakutani fixed point theorem : Let Γ : X → X be a multi-function from a simplex X into itself ; if Γ can be factorized by an arbitrary finite number of Kakutani multifunctions, then Γ has a fixed point. The proof relies on a simplicial approximation technique and the Brouwer fixed point theorem. Extensions to infinite-dimensional spaces and applications to game theory are given. |
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| 1 : | Laboratoire de Mathématiques Informatique et Applications (LAMIA) |
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Université des Antilles et de la Guyane |
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| Domaine | : | Mathématiques/Analyse fonctionnelle |
| hal-00699225, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00699225 | |
| oai:hal.archives-ouvertes.fr:hal-00699225 | |
| Contributeur : Marc Lassonde | |
| Soumis le : Dimanche 20 Mai 2012, 06:17:13 | |
| Dernière modification le : Dimanche 20 Mai 2012, 06:17:13 | |
