New perturbed finite step iterative algorithms for a system of extended generalized nonlinear mixed quasi-variational inclusions

This paper introduces a new system of extended generalized nonlinear mixed quasivariational inclusions involving A-maximal m-relaxed η-accretive (so called (A, η)-accretive (Lan et al. (2006) [37])) mappings in q-uniformly smooth Banach spaces. By using the resolvent operator technique for A-maximal m-relaxed η-accretive mappings due to Lan et al., we establish the existence and uniqueness of solution for this system of extended generalized nonlinear mixed quasi-variational inclusions and construct a new perturbed N-step iterative algorithm with mixed errors for solving the mentioned system. We also prove the convergence of the sequences generated by our algorithms in q-uniformly smooth Banach spaces. The results presented in this paper extend and improve some known results in the literature.