Abstract
This paper introduces a new system of extended generalized nonlinear mixed quasi-variational 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.
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