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An extension of Brouwer's fixed point theorem allowing discontinuities
[Une extension du théorème du point fixe de Brouwer autorisant des discontinuités]

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  • Philippe Bich

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

In this article, we extend Brouwer's fixed point theorem-which states that every continuous mapping from a convex compact subset of a Euclidean space to itself must have a fixed point, by allowing discontinuities of the function, and we apply this extension to equilibrium theory in Economics.

Suggested Citation

  • Philippe Bich, 2004. "An extension of Brouwer's fixed point theorem allowing discontinuities [Une extension du théorème du point fixe de Brouwer autorisant des discontinuités]," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01396169, HAL.
    • Handle: RePEc:hal:cesptp:hal-01396169
    DOI: 10.1016/j.crma.2004.03.001
    Note: View the original document on HAL open archive server: https://hal.science/hal-01396169
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    References listed on IDEAS

    as
    1. Hirsch, M. D. & Magill, M. & Mas-Colell, A., 1990. "A geometric approach to a class of equilibrium existence theorems," Journal of Mathematical Economics, Elsevier, vol. 19(1-2), pages 95-106.
    2. Duffie, Darrell & Shafer, Wayne, 1985. "Equilibrium in incomplete markets: I : A basic model of generic existence," Journal of Mathematical Economics, Elsevier, vol. 14(3), pages 285-300, June.
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    Keywords

    Brouwer; Discontinuities;

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