Error bounds of regularized gap functions for weak vector variational inequality problems

where C ⊆ Rm is a closed convex and pointed cone with nonempty interior intC. (WVVI) was firstly introduced by Giannessi []. It has been shown to have many applications in vector optimization problems and traffic equilibrium problems (e.g., [, ]). Error bounds are to depict the distance from a feasible solution to the solution set, and have played an important role not only in sensitivity analysis but also in convergence analysis of iterative algorithms. Recently, kinds of error bounds have been presented for weak vector variational inequalities in [–]. By using a scalarization approach of Konnov [], Li and Mastroeni [] established the error bounds for two kinds of (WVVIs) with setvalued mappings. By a regularized gap function and a D-gap function for a weak vector variational inequality, Charitha and Dutta [] obtained the error bounds of (WVVI), respectively. Recently, in virtue of the regularized gap functions, Sun and Chai [] studied some error bounds for generalized (WVVIs). By using the image space analysis, Xu and Li [] got a gap function for (WVVI). Then, they established an error bound for (WVVI) without the convexity of the constraint set. These papers have a common characteristic: the solution set of (WVVI) is a singleton [, ]. Even though the solution set of (WVVI) is not a singleton [, ], the solution set of the corresponding variational inequality (VI) is a singleton, when their results reduce to (VI). In this paper, by the nonlinear scalarization method, we study a global error bound of (WVVI). This paper is organized as follows. In Section , we establish a global error bound