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On the existence and approximation of solutions for bilevel vector variational inequalities in Banach spaces

. In this paper, a bilevel vector variational inequality problem is investigated in the setting of Banach spaces. We propose a method which consists in reducing the study of the bilevel vector variational inequality problem to that of a one level vector problem. By introducing a vector auxiliary principle, we propose an algorithm to approximate the solution of the considered bilevel vector variational inequality problem. The strong convergence of the proposed iterative method is studied.