Infinite-dimensional Gale-Nikaido-Debreu theorem and a fixed-point theorem of Tarafdar

This paper proves the equivalence of five fixed-point theorems in topological vector spaces and then uses them to deduce an infinite-dimensional generalization of the classic Gale-Nikaido-Debreu theorem. The proof is based on the Hahn-Banach theorem and the Tarafdar fixed point theorem. There is also a discussion of the relationship of this generalization to the existence theorems of Aliprantis and Brown, Border, Yannelis and others.