An extension of Brouwer's fixed point theorem allowing discontinuities

Philippe Bich

doi:10.1016/j.crma.2004.03.001

Mathematical Analysis/Mathematical Economics

An extension of Brouwer's fixed point theorem allowing discontinuities

Presented by: Pierre-Louis Lions

Philippe Bich ¹

¹ CEREMADE, 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.

Abstract
Résumé

In this article, we extend Brouwer's fixed point theorem – which states that every continuous mapping $f : B \to B$ (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: 2003-10-30
Accepted: 2004-03-02
Published online: 2004-04-12

DOI: 10.1016/j.crma.2004.03.001

Author's affiliations:

Philippe Bich ¹

¹ CEREMADE, Université de Paris Dauphine, place du Maréchal de Lattre de Tassigny, 75775 Paris cedex 16, France

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     title = {An extension of {Brouwer's} fixed point theorem allowing discontinuities},
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     doi = {10.1016/j.crma.2004.03.001},
     language = {en},
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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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.03.001/

References
Cited by

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