Open Access

Fixed-point-like theorems on subspaces

Fixed Point Theory and Applications20042004:602917

https://doi.org/10.1155/S1687182004406056

Received: 8 June 2004

Published: 26 August 2004

Abstract

We prove a fixed-point-like theorem for multivalued mappings defined on the finite Cartesian product of Grassmannian manifolds and convex sets. Our result generalizes two different kinds of theorems: the fixed-point-like theorem by Hirsch et al. (1990) or Husseini et al. (1990) and the fixed-point theorem by Gale and Mas-Colell (1975) (which generalizes Kakutani's theorem (1941)).

Authors’ Affiliations

(1)
Centre de Recherche en Mathématiques de la Décision, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny
(2)
Centre de Recherche en Mathématiques, Statistique et Economie Mathématique, Université Paris 1

Copyright

© Bich and Cornet 2004