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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
91B50 General equilibrium theory
47H04 Set-valued operators
47N10 Applications of operator theory in optimization, convex analysis, mathematical programming, economics
47J35 Nonlinear evolution equations
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