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Fixed point and maximal element theorems with applications to abstract economies and minimax inequalities. (English) Zbl 1033.47039
The authors establish some fixed point theorem for a family of multivalued operators. From these results, some maximal element theorems for a family of φ-condensing multivalued operators are derived. Applications to equilibrium theory in generalized abstract economies and to minimax inequalities are also presented.

MSC:
47H10Fixed point theorems for nonlinear operators on topological linear spaces
91B50General equilibrium theory in economics
47H04Set-valued operators
47N10Applications of operator theory in optimization, convex analysis, programming, economics
47J35Nonlinear evolution equations