Infinite-dimensional Gale-Nikaido-Debreu theorem and a fixed-point theorem of Tarafdar. (English) Zbl 0646.47036

In the first part of their paper the authors give a list of five statements on fixed points for multivalued mappings defined in linear topological spaces and prove that they imply each other. One of them, a theorem of G. Tarafdar from [Proc. Am. Math. Soc. 67, 95-98 (1977; Zbl 0369.47029)] is used in the second part to prove an infinite dimensional version of the Gale-Nikaido-Debreu theorem that occurs in mathematical economics. The theorem proved is more general than another infinite dimensional version of G.-N.-D. theorem given by N. C. Yannelis [J. Math. Anal. Appl. 108, 595-599 (1985; Zbl 0581.90010)]. One of the tools used in the proof is the Hahn-Banach theorem.
Reviewer: M.Sablik


47H10 Fixed-point theorems
91B50 General equilibrium theory
54H25 Fixed-point and coincidence theorems (topological aspects)
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