Coincidence theorem and existence theorems of solutions for a system of Ky Fan type minimax inequalities in FC-spaces

Abstract

Let $I$ be any index set. By using some existence theorems of maximal elements for a family of set-valued mappings involving a better admissible set-valued mapping under noncompact setting of $FC$-spaces, we first present some nonempty intersection theorems for a family $\{G_{i}\}_{i\in I}$ in a product space of $FC$-spaces. Next we give a coincidence theorem and a Fan-Browder type fixed point theorem. Finally, as applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems are proved in product $FC$-space, some existence theorems of solutions for a system of Ky Fan type minimax inequalities involving a family of $G_{\cal B}$-majorized mappings defined on the product space of $FC$-space are also obtained. Our results improve and generalize some recent results.