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We introduce a new system of generalized nonlinear mixed quasivariational inequalities and prove the existence and uniqueness of the solution for the system in Hilbert spaces. The main result of this paper is an extension and improvement of the well-known corresponding results in Kim-Kim [16], Noor [21]-[23] and Verma [24]-[26].

A NEW SYSTEM OF GENERALIZED NONLINEAR MIXED QUASIVARIATIONAL INEQUALITIES AND ITERATIVE ALGORITHMS IN HILBERT SPACES