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Vector Variational Inequalities

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The vector variational inequality is a mathematics model which is designed to account for equilibrium situations where the multicriteria consideration is important. The concept of a vector variational inequality was introduced in [5]. In recent years, the vector variational inequality problem has received extensive attentions and found many applications in vector optimization and vector network equilibrium problems. The theory of vector variational inequalities has been summarized in the edited book [7] and one chapter of the monograph [1].

Let X and Y be Hausdorff topological vector spaces. By L(X, Y), we denote the set of all linear continuous functions from X into Y. For lL(X,Y), the value of linear function l at x is denoted by l,x. Let CY be a nonempty, pointed, closed and convex cone with intC≠∅. For convenience, we will denote C\{0} and intC by C o and respectively. Then (Y,C) is an ordered Hausdorff topological