Hartman-Stampacchia theorem, Gale-Nikaido-Debreu lemma, and Brouwer and Kakutani fixed-point theorems

Pascal Gourdel (), Cuong Le Van (), Ngoc-Sang Pham and Cuong Tran Viet ()
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Pascal Gourdel: PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique
Cuong Le Van: IPAG Business School, CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement

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Abstract: This paper uses the Hartman-Stampacchia theorems as the primary tool to prove the Gale-Nikaidô-Debreu lemmas. It also establishes a cycle of equivalences among the Hartman-Stampacchia theorems, the Gale-Nikaidô-Debreu lemmas, and Kakutani and Brouwer fixed-point theorems.

Keywords: Hartman-Stampacchia theorem; Gale-Nikaido-Debreu lemma; Brouwer fixed point theorem; Kakutani fixed point theorem; General equilibrium; Variational inequalities (search for similar items in EconPapers)
Date: 2026-04-06
Note: View the original document on HAL open archive server: https://hal.science/hal-04008394v3
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Related works:
Journal Article: Hartman–Stampacchia Theorems, Gale–Nikaidô–Debreu Lemma, and Brouwer and Kakutani Fixed-Point Theorems (2026)
Working Paper: Hartman-Stampacchia theorem, Gale-Nikaido-Debreu lemma, and Brouwer and Kakutani fixed-point theorems (2026)
Working Paper: Hartman-Stampacchia theorem, Gale-Nikaido-Debreu lemma, and Brouwer and Kakutani fixed-point theorems (2023)
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