KKM Theorem, Coincidence Theorem And Equilibrium Existence Theorem

This paper mainly further studies KKM type theorem, coincidencetheorem and equilibrium problem of abstract economies in topological spaces,it also unites and generalizes some known results in recent literatures. Firstly,some new KKM type theorems with finitely closed values are established intopological spaces. By applying these new KKM type theorems, some newKyFan type minimax inequalities and saddle points theorems are proved intopological spaces. Secondly, by applying the technique of continuous partitionof unity, some coincidence theorems for involving a better admissible mapping onthe product FC-spaces are proved. Lastly, several new fixed points theorems areproved in FC-spaces. By applying these theorems, some new minimax inequali-ties and existence theorems of maximal elements are established in FC-spaces.Finally, by applying the existence theorems of maximal elements, some newequilibrium existence theorems of abstract economies are obtained in FC-spaces.