Stability Of Solution Sets For Vector Equilibrium Problems

Vector equilibrium problem is an important branch of nonlinear functional analysis,and it has been widely used in many domains,such as transportation,financial engineering,human resources,etc.In this thesis,we study two classes of problems:the stability of solution sets for vector equilibrium problem and vector variational inequality problems.This thesis is divided into four chapters,the main contents are as follows:In chapter 1,we introduce the background and research status of the stability of solu-tion sets for vector equilibrium problems and vector variational inequalities,and list some common symbols,basic concepts and lemmas which are used in this thesis.In chapter 2,we consider the weak upper semi-continuity of solution sets for vector equilibrium problems in reflexive Banach spaces.Firstly,when the constrained set and the mapping are perturbed by different parameters simultaneously,vector equilibrium problem is transformed into convex optimization problem by using the gap function of vector equilibrium problem,then the weak upper semi-continuity of solution sets for vector equilibrium problem is established.Secondly,we transform mixed vector variational inequality problem into equilibrium problem,the stability of solution sets for mixed vector variational inequality is obtained according to the stability of solution sets for vector equilibrium problem.In chapter 3,we study the stability of solution sets for vector variational inequalities in reflexive Banach spaces.Under the condition that the constraint set and the mapping are perturbed by different parameters simultaneously.the results of the weak upper semi-continuity and closeness of solution sets for vector variational inequalities are established when J-g o F and F are the compact and upper semi-continuous mapping,respectively.In chapter 4,in the Rn space,when the constraint set and the mapping are perturbed by different parameters simultaneously,the lower semi-continuity of solution sets for vec-tor variational inequalities is obtained by using the topological degree of vector variational inequalities.Compared with some previous results,any monotone-type or strict monotone-type assumptions of the mapping involved,and any compact assumptions of the sets involved are not required.