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The purpose of this paper is to introduce new approximation methods for solutions of generalized non-accretive multi-valued mixed quasi-variational inclusion systems involving (A,η)-accretive mappings in q-uniformly smooth Banach spaces and, by using the new resolvent operator technique associated with (A,η)-accretive mappings, Nadler’s fixed point theorem and Liu’s inequality, we prove some existence theorems of solutions for our systems by constructing the new Mann iterative algorithm. Further, we study the stability of the iterative sequence generated by the perturbed iterative algorithms. The results presented in this paper improve and generalize the corresponding results of recent works given by some authors.

Approximation methods for solutions of generalized multi-valued mixed quasi-variational inclusion systems