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

Pascal Gourdel; Van, Cuong Le; Ngoc‐Sang Pham; Cuong Tran Viet

doi:10.48550/arxiv.2604.05603

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

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Pascal Gourdel, Van, Cuong Le, Ngoc‐Sang Pham, Cuong Tran Viet

DOI: 10.48550/arxiv.2604.05603

Cited by: 2

Abstract

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

Fields of Study & Subjects

Fixed Point Theorems Analysis Stability and Control of Uncertain Systems

Publication details

Journal / source: arXiv (Cornell University)
Publication date: 7 April 2026
Language: EN
Document type: Preprint