an:04054395
Zbl 0646.47036
Mehta, Ghanshyam; Tarafdar, Enayet
Infinite-dimensional Gale-Nikaido-Debreu theorem and a fixed-point theorem of Tarafdar
EN
J. Econ. Theory 41, 333-339 (1987).
00152653
1987
j
47H10 91B50 54H25
fixed points for multivalued mappings defined in linear topological spaces; infinite dimensional version of the Gale-Nikaido-Debreu theorem; mathematical economics; Hahn-Banach theorem
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 \textit{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 \textit{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.
M.Sablik
Zbl 0369.47029; Zbl 0581.90010