Existence and algorithm of solutions for mixed quasi-variational-like inclusions in Banach spaces

In this paper, we study a class of mixed quasi-variational-like inclusion with a bifunction in reflexive Banach spaces. By applying a minimax inequality due to the first author, some existence and uniqueness theorems of solutions for the mixed quasi-variational-like inclusions are proved. Next, by applying the auxiliary variational inequality technique, we suggest an iterative algorithm to compute the approximate solutions of the mixed quasi-variational-like inclusions. The convergence criteria of the algorithm is studied under quite mild conditions. Our results represent improvement and generalization of the previously known results in literature.