Hartman-Stampacchia theorems, Gale-Nikaido-Debreu lemmas, and Brouwer/Kakutani fixed-point theorems are equivalent via a cycle of implications.
The Quarterly Journal of Econ omics 104(2), 385–389 (1989) 19Indeed, if p = 0 , then ⟨p, z⟩ ≤ 0
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Hartman-Stampacchia theorem, Gale-Nikaido-Debreu lemma, and Brouwer and Kakutani fixed-point theorems
Hartman-Stampacchia theorems, Gale-Nikaido-Debreu lemmas, and Brouwer/Kakutani fixed-point theorems are equivalent via a cycle of implications.