Fixed Point Theory and Applications 
Volume 2004 (2004), Issue 3, Pages 159-171
doi:10.1155/S1687182004406056

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

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)).