Fixed Point Theorem and Supinfsup Inequalities in FC-Space Without Compactness

A new finite intersection theorem was obtained by KKM type theorem in FC-spaces,as its application, a fixed point theorem is proved in FC-spaces and the problem of von Neumann-Fan type supinfsup inequalities(equalities)for multimap in FC-spaces without compactness were discussed as applications.These theorems generalize some known results in recent literatures.