The Existence Of Solution Of Generalized Vector Variational Inequalities With Set-valued Mapping

As an important branch of mathematics, variational inequalities are applied to the field of operational research, computer science, engineering technology, transportation, economics and management et.al.Generalized vector variational inequalities with set-valued mapping, involving mathematical economics, mechanics, physics, fiance and control theory and so on, are generation of variational inequalities. They become significant foundation and tool for studying multiobjective programe, equilibrium and traffic problems, so they are hot spots in the field of applied mathematics. Because generalized vector variational inequlities touch upon many mathematical branches, such as fuctional analysis, convex analysis and variational analysis, the research for them is of much academic value and certain of degree of difficult. This dissertation is devoted to study generalized vector variational inequalities, the unity and extension of a number of well-known vector variational inequalities, in Banach spaces and Hausdorff topological vector spaces. The main results, obtained in this dissertation can be summarized as follows:1. In chapter 1,we introduce the background and the state of the field of generalized vector variational inequalities compendiously. Basing on the former theory, we propose two classes of generalized vector variational inequalities with set-valued mapping, and we obtain this dissertation.2. In chapter 2, the existence of solution for generalized vector variational inequality in Banach space is discussed.Find x∈K,such that (?)s∈T(x),Firstly, making use of the new concepts ofη-hemicontinuous and Ky Fan lemma,the existence of solution of (GVVTI) under the assumption of pseudomonotone is proved. Secondly, by means of the known Brouwer fixed point theorem and Browder fixed point theorem, we established the existence of solutions for (GVVTI) without pseudomonotone in this dissertation.3. Chapter 3 is devoted to study another class of generalized vector variational inequalitieswith set-valued mapping, which is the improvement of (GVVTI) in Hausdorfftopological vector space. Because of the improvement, we established a functionBy applying the concept of L_s-majored and KF mapping, the existence of solution of(GVVTI) is proved without pseudomonotone, firstly. Then, by means of the transferred closed mapping, the existence of solution is obtained under the assumption of pseudomonotone.4. In chapter 4, we summarize the results.