Vector Equilibrium Problems For Further Research

This text mainly study the strong vector equilibrium problems,the generalized vector equilibrium problems , the generalized vector quasi-equilibrium problems and the parametric vector equilibrium problem, made by the Fan-KKM theorem,the generalized section theorem and the generalized Fan-Browde fixed point theorem.1. Mainly study the strong vector equilibrium problems and the generalized vector equilibrium problems under restricted conditions. Section 1, for prepare knowledge.In section 2, we get an existent theorem of the strong vector equilibrium problem by positive function and Fan Ky inequality theorem. In section 3 , we get an existent theorem of the generalized vector equilibrium problem under restricted conditions in two different spaces by the generalized Kakutani fixed point theorem.2. Mainly study the parametric vector equilibrium problems, the generalized vector equilibrium problems and the generalized vector quasi-equilibrium problems in the sence ofC_x - quasiconvex-like.In section 4,firstly we prove a parametric vector equilibrium problemby Fan-KKM theorem;secondly we also prove the mapping from the space of paramer to that of its solution is upper hemi-continuous,and then we prove the mapping from function space of f to X is also upper hemi-continuous,we prove the generic stability in it. In section 5, firstly we prove the existence of generalized vector equilibrium prolems by Fan-KKM theorem,and we discuss the property of its solution set;secondly we prove the existence of generalized vector equilibrium problem by the Fan-Browde fixed point theorem. In section 6,we we prove the existence of generalized vector quasi-equilibrium problem by the generalized Fan-Browde fixed point theorem.