Fixed-point-like theorems on subspaces

Philippe Bich () and Bernard Cornet
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Philippe Bich: CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique
Bernard Cornet: CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique

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Abstract: In this paper, we prove a fixed-point-like theorem for multi-valued mappings defined on the finite Cartesian product of Grassmannian manifolds and convex sets. Our result generalizes two different kinds of theorems: the fixedpoint-like theorem by Hirsh, Magill, Mas-Colell (1990) or Husseiny, Lasry, Magill (1990) and the fixed-point theorem by Gale, Mas-Colell (1975) (which generalizes Kakutani's theorem (1941)).

Keywords: fixed-point; Grassmannian manifold; degree theory; point-fixe; Grassmanienne; théorie du degré (search for similar items in EconPapers)
Date: 2004-06
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-03330770v1
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Citations: View citations in EconPapers (11)

Published in 2004

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-03330770

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