Fixed-point-like theorems on subspaces

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)).