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

✍ Scribed by Xie Ping Ding

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 275 KB
• Volume: 67
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2006.06.037

✦ Synopsis

Let I be any index set. Some new families of G KKM -mappings and G KKM -majorized mappings from a topological space X into finite continuous topological spaces (Y i , ϕ N i ) (in short, FC-spaces) involving a set-valued mapping T ∈ KKM(Y, X ) with KKM property are introduced where Y = i∈I Y i . Some existence theorems of maximal elements for the families of G KKMmajorized mappings and G KKM -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.