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arXiv · 2604.05603

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

Pascal Gourdel·Cuong Le Van·Ngoc-Sang Pham·Cuong Tran Viet
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Abstract

This paper uses the Hartman-Stampacchia theorems as the primary tool to prove the Gale-Nikaid{\^o}-Debreu lemmas. It also establishes a cycle of equivalences among the Hartman-Stampacchia theorems, the Gale-Nikaid{\^o}-Debreu lemmas, and Kakutani and Brouwer fixed-point theorems.

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Pascal Gourdel, Cuong Le Van, Ngoc-Sang Pham, Cuong Tran Viet. 2026-04-07. Hartman-Stampacchia theorem, Gale-Nikaido-Debreu lemma, and Brouwer and Kakutani fixed-point theorems. https://arxiv.org/abs/2604.05603

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