Bulletin of the
Korean Mathematical Society BKMS

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 present some non\-empty intersection theorems for a family $\{G_{i}\}_{i\in I}$ in product $FC$-spaces. Then, as applications, some new existence theorems of equilibrium for a system of generalized vector equilibrium problems are proved in product $FC$-spaces. Our results improve and generalize some recent results.

Keywords: maximal element, nonempty intersection theorem, system of generalized vector equilibrium problems, product $FC$-space

MSC numbers: 49J40, 49J53