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

Gourdel, Pascal and Le Van, Cuong and Pham, Ngoc-Sang and Tran Viet, Cuong (2023): Hartman-Stampacchia theorem, Gale-Nikaido-Debreu lemma, and Brouwer and Kakutani fixed-point theorems.

Abstract

This paper uses the Hartman-Stampacchia theorems as primary tool to prove the Gale-Nikaido-Debreu lemma. It also establishes a full equivalence circle among the Hartman Stampacchia theorems, the Gale-Nikaido-Debreu lemmas, and Kakutani and Brouwer fixed point theorems.

• Item Type: MPRA Paper
• Language: English
• Keywords: Hartman-Stampacchia theorem, Gale-Nikaido-Debreu Lemma, Brouwer fixed points theorem, Kakutani fixed points theorem.
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C60 - General; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C62 - Existence and Stability Conditions of Equilibrium; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C65 - Miscellaneous Mathematical Tools; D - Microeconomics > D5 - General Equilibrium and Disequilibrium

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