Maximal elements of image-majorized mappings in product image-spaces and applications (I) Original Research Article

Let II be any index set. Some new families of View the MathML sourceGKKM-mappings and View the MathML sourceGKKM-majorized mappings from a topological space XX into finite continuous topological spaces (Yi,φNi)(Yi,φNi) (in short, View the MathML sourceFC-spaces) involving a set-valued mapping View the MathML sourceT∈KKM(Y,X) with KKM property are introduced where Y=∏i∈IYiY=∏i∈IYi. Some existence theorems of maximal elements for the families of View the MathML sourceGKKM-majorized mappings and View the MathML sourceGKKM-mappings are proved under noncompact setting of product View the MathML sourceFC-spaces. As applications, some new equilibrium existence theorems of generalized games are established in noncompact product View the MathML sourceFC-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.