The Property Of The Solution For Vetor Equilibrium Problems In Lexicographic Order

In this thesis, we study two problems: lexicographic vector equilibrium and cone saddle point theorem for set-valued mappings. The detailed contents are listed as following:Part one, Discuss the relations between sequential vector equilibrium problem and lexicographic vector equilibrium problem under the background of n-dimensional Euclidean space, Firstly, we introduced a total order, namely lexicographic order. Furthermore, we discussed several vector equilibrium problems, i.e., strong or weak vector equilibrium problem, sequential vector equilibrium problem and lexicographic vector equilibrium problem, as well as the relationship among their solution sets. Finally, Existence result for a lexicographic vector equilibrium problem is obtained from that of a sequential vector equilibrium problem.Part two, In Hausdorff topological vector space, we discuss some existence theorems for Benson cone saddle points of vector-valued mappings and a cone loose saddle point theorem for set-valued mappings. A Benson cone saddle point theorem for vector-valued mappings is first established by virtue of the Kakutani-Fan-Glicksberg fixed point theorem and a nonlinear scalarization function. Then a cone loose saddle point theorem for set-valued mappings is also obtained by using the Kakutani-Fan-Glic ksberg fixed point theorem.