The Research Of A Class Of Equilibrium Problems

Equilibrium problems theory provide us with a unified, natural, innovative and general framework to study a wide class of problems arising in finance, economics, network analysis, transportation and optimization. Since it contains the extensiveness of problem and the deepness that solves problem to make the vector equilibrium and optimization problems of various types, gets maximum solicitude. In recent years,various vector equilibrium optimization problems get extensive and thorough research, a lot of results in many aspects such as economic equilibrium theory, game theory and economic management get extensive application and show its importance gradually. Become an important key content of goal program theoretical research.The solution existence of equilibrium problems is the kernel of the study of the theory of equilibrium. According to the existence results of general equilibrium problems and vector equilibrium problems have been studied more and more. Inspired and motivated by these research results, this paper is devoted to study systematically a class of equilibrium problems, which is unify and extension of a large number of known equilibrium problems and variational inequalities problems. The research is carried on from three aspects.Firstly, in finitely continuous topological spaces, we introduce four new types of the system of generalized vector quasi-equilibrium problems, and we derive some existence results of a solution for the system of generalized vector quasi-equilibrium problems via the maximal element theorems in product finitely continuous topological spaces.Secondly, in complete metric spaces, we provide the Ekeland variational principle to equilibrium problems with set-valued maps. And via the Ekeland variational principle, existence results for vector equilibrium problem with set-valued maps and the system of vector equilibrium problem with set-valued maps.Lastly, in a real topological vector spaces, we introduce the topological pseudomonotonicity to a class of vector valued trifunctions, and derive someexistence results for the system of generalized vector equilibrium problems via topological pseudomonotonicity and generalized H-KKM theorem.