Gap Funciton And Existence Of Solutions For A System Of Generalized Vector Equilibrium Problems

The equilibrium problems contain as special cases Nash equilibrium problems, fixed pointproblems, optimization and control problems, variational inequality and complementarityproblems. Actually they are widely used in many fields as well as greatly achieved academicvalue. This thesis is devoted to studying the existence of gap functions for the generalized vectorequilibrium problem and the system of generalized vector equilibrium problems, some existenceresults for the system of generalized vector equilibrium problems are proved by virtue of thenonlinear scalarization function.The main results here can be summarized as follows:In Chapter2, the gap functions and generalized gap functions for several kinds of vectorequilibrium problems in Hausdorff topology spaces are introduced. Furthermore, by makinguse of the properties of nonlinear scalarization function, the gap functions for the system ofgeneralized vector equilibrium problems are obtained.In Chapter3, the existence of solution to the system of generalized vector equilibriumproblems is proved and the gap functions for system of generalized vector equilibrium problemswith set-valued mappings are given by using nonlinear scalarization function. Moreover, someexistence results for the system of generalized vector equilibrium problems are proved andsome necessary and sufficient conditions for the system of generalized vector equilibriumproblems are established.