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Vietnam Journal of Mathematics 36:4(2008) 437-449  Some Generalized Quasi-Ky Fan Inequalities in Topological Ordered Spaces Nguyen The Vinh Abstract.  In this paper, we obtain some existence results for solutions of some generalized quasi-Ky Fan inequalities and Nash equilibrium points for a game system in topological semilattices. Our results are similar to the ones obtained by Luo under some other conditions about continuity and convexity of vector set-valued mappings.   1991 Mathematics Subject Classification: 46N10, 47J20, 54H25, 54C60, 91B50. Keywords: Fan-Browder fixed point theorem, set-valued mapping, minimax inequality, topological semilattices, $C$-$\Delta$-quasiconvex (quasiconcave), upper (lower) $C$-continuous, generalized Nash equilibrium point.

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