Existence of solutions and convergence of iterative algorithms for a system of generalized nonlinear mixed quasi-variational inclusions

Abstract

In this paper, we introduce and study a new system of generalized nonlinear mixed quasi-variational inclusions in q -uniformly smooth Banach spaces. We prove the existence and uniqueness of solutions for this system of generalized nonlinear mixed quasi-variational inclusions. We also prove the convergence of several new two-step iterative algorithms with or without errors for this system of generalized nonlinear mixed quasi-variational inclusions. The results in this paper extend and improve some known results in the literature.