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

Tarafdar, E.

Commentat. Math. Univ. Carol. 31, No. 4, 723-730 (1990).

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)

MSC:

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

Keywords:

fixed point theorems for multivalued mappings in locally convex spaces; 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