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Fixed-point-like theorems on subspaces

Fixed Point Theory and Applications volume 2004, Article number: 602917 (2004) Cite this article

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)).

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Authors and Affiliations

  1. Centre de Recherche en Mathématiques de la Décision, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, Paris, 75775, France

    Philippe Bich

  2. Centre de Recherche en Mathématiques, Statistique et Economie Mathématique, Université Paris 1, 106-112 boulevard de l'Hôpital, Paris, 75647, France

    Bernard Cornet

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  1. Philippe Bich
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  2. Bernard Cornet
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Correspondence to Philippe Bich.

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Bich, P., Cornet, B. Fixed-point-like theorems on subspaces. Fixed Point Theory Appl 2004, 602917 (2004). https://doi.org/10.1155/S1687182004406056

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  • DOI: https://doi.org/10.1155/S1687182004406056