Existence Of Solutions To Generalized Vector Quasi-equilibrium Problems

Today, vector equilibrium problem is a hot issue in the field of operations research and nonlinear analysis research. Vector equilibrium problem contains vector variational inequalities, vector optimization, vector Nash equilibrium and vector complementarity problems as special cases. At present, for vector variational inequalities research matures gradually, vector equilibrium problem have been intensively stuided by many scholars. Research in this field of vector equilibrium problems mainly related to three aspects, namely existence of solutions to equilibrium problems, an iterative algorithm for solving equilibrium problem is structured and then prove the convergence and stability analysis of the solutions. Generalized vector quasi-equilibrium problems is generalizing forms of vector equilibrium problems. It is of great significance.In this thesis, we study a class of existence of solutions to generalized vector quasi-equilibrium problems and existence of solutions to set-valued generalized strong vector quasi-equilibrium problems, meanwhile, existence of solutions to a generalized multivalued vector variational-like inequalities are also considered. These results generalize the corresponding results in related literatures.In chapter 2, we study a class of generalized vector quasi-equilibrium problems and a generalized multivalued vector variational-like inequality problems. First, we use the maximal element theorem with an escaping sequence to prove the existence results of solutions for the class of generalized vector quasi-equilibrium problems without any monotonicity conditions in the setting of locally convex topological vector space; Next, it is devoted to introduce a generalized multivalued vector variational-like inequality and obtain some existence results under the condition of lower semicontinuity of the multivalued mapping in Banach spaces. The last result is proved by using the concept of escaping sequence without any compactness condition of the set and famous KKM theorem. The results improve and extend the correspon results of related literatures.In chapter 3, under the conditions of naturally quasi C- convex, the definition of lower ? C?--contimuity and the Kakutani-Fan-Glicksberg fixed point theorem, an existence theorem for solutions to set-valued generalized strong vector quasi-equilibrium problems was established,without the assumption that the dual cone?C of the ordering cone C has a weak-star compact base. These results generalize some recent results in this field.