| Auteur(s) |
Marc Lassonde ( )1 |
| Laboratoire |
|
| Domaine |
Mathématiques/Analyse fonctionnelle
|
| Titre |
Fixed points for Kakutani factorizable multifunctions |
| Résumé |
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. |
| Langue du texte intégral |
Anglais |
|
| Journal |
Journal of Mathematical Analysis and applications |
| Audience |
internationale |
| Date de publication |
1990 |
| Volume |
152 |
| Numéro |
1 |
| Page, identifiant, ... |
46-60 |
|
|
