Generalizations of the FKKM theorem and the Ky Fan minimax inequality, with applications to maximal elements, price equilibrium, and complementarity. (English) Zbl 0767.49007

The paper presents a generalization of the FKKM theorem of Fan by introducing generalized closedness and continuity conditions. Then, this theorem is used to extend the Ky Fan minimax inequality by relaxing compactness, convexity and lower semicontinuity assumptions. Finally, some applications of these results to existence theorems in economics and optimization theory are given.


49J45 Methods involving semicontinuity and convergence; relaxation
54H25 Fixed-point and coincidence theorems (topological aspects)
91B50 General equilibrium theory
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
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