Comptes Rendus
no. 9
Mathematical Analysis/Mathematical Economics
An extension of Brouwer's fixed point theorem allowing discontinuities
Pierre-Louis Lions
Philippe Bich1
1CEREMADE, Université de Paris Dauphine, place du Maréchal de Lattre de Tassigny, 75775 Paris cedex 16, France
Comptes Rendus. Mathématique, Volume 338 (2004) no. 9, pp. 673-678

In this article, we extend Brouwer's fixed point theorem – which states that every continuous mapping f:B→B (a closed ball of ℝ n ) must have a fixed point – by allowing discontinuities of f, and we apply this extension to equilibrium theory in Economics.

Nous étendons dans cet article le théorème du point fixe de Brouwer – qui dit que toute fonction f continue de B dans B (une boule fermée de ℝ n ) admet un point fixe – en autorisant un certain type de discontinuité de f sur un ensemble éventuellement infini, et appliquons cette extension à la théorie de l'équilibre général en économie.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2004.03.001

Philippe Bich  1

1 CEREMADE, Université de Paris Dauphine, place du Maréchal de Lattre de Tassigny, 75775 Paris cedex 16, France 
Philippe Bich. An extension of Brouwer's fixed point theorem allowing discontinuities. Comptes Rendus. Mathématique, Volume 338 (2004) no. 9, pp. 673-678. doi: 10.1016/j.crma.2004.03.001
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