An extension of Fan’s fixed point theorem and equilibrium point of an abstract economy. (English) Zbl 0745.47046

The article deals with some fixed point theorems for multivalued mappings in locally convex spaces and their economical applications. The main topic is a new generalization of K. Fan’s fixed point theorem for almost upper semicontinuous mappings, Debreu and Shafer-Sonnenschein theorems on equilibrium points for the case of economics in locally convex topological vector spaces.
Reviewer: P.Zabreiko (Minsk)


47H10 Fixed-point theorems
91B50 General equilibrium theory
47H04 Set-valued operators
52A07 Convex sets in topological vector spaces (aspects of convex geometry)
49J35 Existence of solutions for minimax problems
49K35 Optimality conditions for minimax problems
91B08 Individual preferences
91B16 Utility theory
Full Text: EuDML