On a new system of generalized mixed quasi-variational-like inclusions with [formula omitted]-accretive operators in real [formula omitted]-uniformly smooth Banach spaces

Abstract

In this paper, we introduce and study a new system of generalized mixed quasi-variational-like inclusions with ( H , η ) -accretive operators which contains variational inequalities, variational inclusions, systems of variational inequalities and systems of variational inclusions in the literature as special cases. By using the resolvent technique for the ( H , η ) -accretive operators, we prove the existence of solutions and the convergence of a new p -step iterative algorithm for this system of generalized mixed quasi-variational-like inclusions in real q -uniformly smooth Banach spaces. The results in this paper unify, extend and improve some known results from the literature.