Maximal elements of GKKM-majorized mappings in product FC-spaces and applications (I)

Let I be any index set. Some new families of GKKM-mappings and GKKM-majorized mappings from a topological space X into finite continuous topological spaces (Yi,φNi) (in short, FC-spaces) involving a set-valued mapping T∈KKM(Y,X) with KKM property are introduced where Y=∏i∈IYi. Some existence theorems of maximal elements for the families of GKKM-majorized mappings and GKKM-mappings are proved under noncompact setting of product FC-spaces. As applications, some new equilibrium existence theorems of generalized games are established in noncompact product FC-spaces. These theorems improve and generalize some recent results in the literature. Some further applications to the system of generalized vector quasi-equilibrium problems will be given in a follow-up paper.