Existence And Stability Of Solutions For Systems Of Generalized Vector Quasi - Equilibrium Problems

The system of generalized vector quasi-equilibrium problems involves broad extent. It contains many model as special cases, such as the variational inequality problem, the qua-sivariational inequality problem, Ky Fan inequality problem, the mulitobjective generalized Nash equilibrium problem, and the system of vector equilibrium problems and so on. In this thesis, we focus on existence and stability for the system of generalized vector quasi-equilibrium problems. This thesis consists of seven chapters.Chapter 1 We introduce some notions and results used in our analysis in this thesis, which are some basic knowledge in nonlinear analysis theory such as continuity and convexity conditions of set-valued maps, essential component definition, and some basic results and so on.Chapter 2 This chapter is devoted to those models for the system of generalized vector quasi-equilibrium problems and its subsystems. First, we introduce the models of the system of generalized vector quasi-equilibrium problems A and the system of generalized vector quasi-equilibrium problems B, which have slight distinction only. Secondly, we introduce some subsystems of the system of generalized vector quasi-equilibrium problems and their relation. Finally, we introduce some kinds of nonlinear equilibrium problems which may be transfered to the system of generalized vector quasi-equilibrium problems.Chapter 3 This chapter is devoted to existence of solutions for the system of generalized vector quasi-equilibrium problems A. By Kakutani-Fan-Glicksberg fixed point theorem, we establish existence results for the system of generalized vector quasi-equilibrium problems and its subsystems. Similarly, we also establish existence results for those nonlinear equilibrium problems which may be transfered to the system of generalized vector quasi-equilibrium problems.Chapter 4 This chapter is devoted to existence of essential components for the system of generalized vector quasi-equilibrium problems A. By defining a distance between two systems of generalized vector quasi-equilibrium problems, we obtain an uniform topological space and establish existence results of essential components for the system of generalized vector quasi-equilibrium problems and its subsystems. Similarly, we also establish existence...