Convergence and stability of iterative algorithm for a new system of (A,η)(A,η)-accretive mapping inclusions in Banach spaces

In this paper, we introduce and study a new system of (A,η)(A,η)-accretive mapping inclusions in Banach spaces. Using the resolvent operator associated with (A,η)(A,η)-accretive mappings, we suggest a new general algorithm and establish the existence and uniqueness of solutions for this system of (A,η)(A,η)-accretive mapping inclusions. Under certain conditions, we discuss the convergence and stability of iterative sequence generated by the algorithm. Our results extend, improve and unify many known results on variational inequalities and variational inclusions.