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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 $\varphi$-condensing multivalued operators are derived. Applications to equilibrium theory in generalized abstract economies and to minimax inequalities are also presented.

##### MSC:
 47H10 Fixed-point theorems for nonlinear operators on topological linear spaces 91B50 General equilibrium theory in economics 47H04 Set-valued operators 47N10 Applications of operator theory in optimization, convex analysis, programming, economics 47J35 Nonlinear evolution equations
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