On a new system of generalized mixed quasi-variational-like inclusions involving (A,η,m)(A,η,m)-accretive operators with applications

In this paper, we introduce a new and interesting system of generalized mixed quasi-variational-like inclusions with (A,η,m)(A,η,m)-accretive operators and relaxed cocoercive mappings which contains variational inequalities, variational inclusions, systems of variational inequalities, systems of variational-like inequalities and systems of variational inclusions in the literature as special cases. By using the resolvent technique for the (A,η,m)(A,η,m)-accretive operators, we prove the existence of solutions and the convergence of a new pp-step iterative algorithm for this system of generalized mixed quasi-variational-like inclusions in real qq-uniformly smooth Banach spaces. The results in this paper unifies, extends and improves some known results in the literature.