Fixed Point Theory and Applications
Volume 2004 (2004), Issue 3, Pages 159-171

Fixed-point-like theorems on subspaces

Philippe Bich1 and Bernard Cornet2

1Centre de Recherche en Mathématiques de la Décision, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, Paris 75775, France
2Centre de Recherche en Mathématiques, Statistique et Economie Mathématique, Université Paris 1, 106-112 boulevard de l'Hôpital, Paris 75647, France

Received 8 June 2004

Copyright © 2004 Philippe Bich and Bernard Cornet. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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)).