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