Iterative algorithms for a new system of nonlinear variational inclusions with (A,η)(A,η)-accretive mappings in Banach spaces

In this paper we introduce and study a new system of nonlinear variational inclusions with (A,η)(A,η)-accretive mappings in Banach spaces. By using the resolvent operator associated with (A,η)(A,η)-accretive mappings, we construct some new iterative algorithms for approximating the solution of this system of variational inclusions. We also prove the existence of solutions and the convergence of the sequences generated by the algorithm in Banach spaces. The results presented in this paper extend and improve some known results in the literature.