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 quasi-variational inclusions involving AA-maximal mm-relaxed ηη-accretive (so called (A,η)(A,η)-accretive (Lan et al. (2006) [37])) mappings in qq-uniformly smooth Banach spaces. By using the resolvent operator technique for AA-maximal mm-relaxed ηη-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 NN-step iterative algorithm with mixed errors for solving the mentioned system. We also prove the convergence of the sequences generated by our algorithms in qq-uniformly smooth Banach spaces. The results presented in this paper extend and improve some known results in the literature.