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