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In this paper, we introduce and study a new class of completely generalized nonlinear mixed quasi-variational inequalities. Using the resolvent operator technique for maximal monotone operators, we construct a perturbed three-step iterative algorithm with errors for solving this kind of completely generalized nonlinear mixed quasi-variational inequalities. Furthermore, we establish a few existence and uniqueness results of solutions for the completely generalized nonlinear mixed quasi-variational inequality involving relaxed Lipschitz, generalized pseudo-contractive and strongly monotone mappings and prove some convergence results of the iterative sequence generated by the perturbed three-step iterative algorithm with errors.

CONVERGENCE OF A PERTURBED THREE-STEP ITERATIVE ALGORITHM WITH ERRORS FOR COMPLETELY GENERALIZED NONLINEAR MIXED QUASI-VARIATIONAL INEQUALITIES