Adv. Math. Econ. Volume 2, pp.87118 (2000)
Fixed point theorems and the existence of economic equilibria based on conditions for local directions of mappings
Ken Urai
Graduate School of Economics, Osaka University, Machikaneyama, Toyonaka, Osaka 5600043, Japan


Fixed point theorems for set valued mappings are reexamined from a
unified viewpoint on local directions of the values of a mapping on a subset of
a Hausdorff topological vector space to itself. Some basic fixed point theorems,
such as Kakutani's and Browder's, are generalized so that we could apply them
to game theoretic and economic equilibrium existence problems with nonordered
preferences having neither global continuity nor convexity conditions. Relations of
our main results to other mathematical theorems such as FanBrowder's theorem,
maximal element existence theorem for Lmajorized mappings, Eaves' theorem,
KKM and KKMS theorem, are also studied.


Kakutani's fixed point theorem, Browder's Rxed point theorem, General equilibrium,
Excess demand, Nonordered preference, Nash equilibrium, Abstract economy,
GaleNikaidoDebreu theorem, Lmajorized mappings, Eaves' Theorem, KKM Theorem, KKMS Theorem.