| In this thesis,we mainly focus on the existence and stability of solutions to vector equilibrium problems.Firstly,with the help of the cosmically upper continuity of conevalued mappings rather than the upper semi-continuity,the existence result of the solutions of symmetric generalized strong vector quasi-equilibrium problems with variable ordering structure is established and a concrete example is given to illustrate the validity of the result.Furthermore,the above result is applied to generalized strong vector saddle point problems,and the existence conclusion of its solutions is obtained.Secondly,we take advantage of some properties of the improvement sets to establish the stability of approximate solutions for parametric bilevel vector equilibrium problems under appropriate conditions,such as upper semi-continuity,lower semi-continuity and Hausdorff lower semi-continuity of solution mappings.These results promote and develop the relevant conclusions of the recent literature.The thesis consists of four chapters as follows.In the first chapter,we mainly introduce the historical research background and development status of the vector equilibrium problem,and then describe the general situation of the problem research and its role and significance in the equilibrium problems.Next,at the end of this chapter,the concepts and lemmas of continuity and known conclusions are given.In the second chapter,we mainly discuss the existence of solutions for symmetric generalized strong vector quasi-equilibrium problems.By means of the cosmically upper continuity condition of the cone-valued mappings rather than the upper semi-continuity condition in the sense of the commonly used set-valued mapping,we apply Fan-KKM theorem and Kakutani-Fan-Glicksberg fixed point theorem to prove the existence theorem of solutions,and then give an example to illustrate the validity of the theorem.Moreover,the result is used to generalized strong vector saddle point problem,and the existence theorem of its solutions is obtained.In the third chapter,we consider the stability of the approximating solutions for the parametric bilevel vector equilibrium problem based on the improvement set.Applying the relevant conclusion of improvement set and flexibly using the properties of the various semi-continuity of set-valued mapping,the conclusion of semi-continuity of approximate solutions mapping for two kinds of the parametric bilevel vector quasi-equilibrium problem is studied under the proper continuity and convexity condition of the equilibrium mapping,including upper semi-continuity,lower semi-continuity and Hausdorff lower semi-continuity.In the fourth chapter,we summarize some research work and results obtained in this paper,and put forward some new problems that worthy of further research. |
