Two Types Of Hybrid Balance Problems In Banach Space Research

Since vector equilibrium problems was introduced, many authors pay attaion on it. Especially the existence and stability theorem of solutions for that kind of problems, and now has made a lot of achievements. Lee、Zeng and Yao and many authors has established some different kinds of vector equilibrium problems, and proved the existence theorem of solutions for them.In this paper, we introduce a new kind of generalized mixed vector equilibrium-type problems(GMVP-TP) in Banach spaces based on previous results. Applying KKM theorem and Nadler’s theorem, we prove the existence theorem of solutions for that kind of problems, which can be used to derive some existence results to some vector variational-like inequalities.In chapter one, we introduced the background, research results and the application of vector variational inequalities, vector equilibrium problems and the existence theorem of solutions of it.In chapter two, we introduced rudimentary knowledge when we start our reseach about vector variational inequalities, vector equilibrium problems and the existence theorem of solutions of it.In chapter three, we established two new kind of generalized mixed vector equilibrium-type problems(GMVP-TP), applying KKM theorem and Nadler’s theorem, we prove the existence theorem of solutions for that kind of problems.