Existence and iterative approximation of solutions of generalized mixed quasi-variational-like inequality problem in Banach spaces

In this paper, some existence theorems for the mixed quasi-variational-like inequalities problem in a reflexive Banach space are established. The auxiliary principle technique is used to suggest a novel and innovative iterative algorithm for computing the approximate solution for the mixed quasi-variational-like inequalities problem. Consequently, not only the existence of theorems of the mixed quasi-variational-like inequalities is shown, but also the convergence of iterative sequences generated by the algorithm is also proven. The results proved in this paper represent an improvement of previously known results.