A generalized forward–backward splitting method for solving a system of quasi variational inclusions in Banach spaces

Abstract

The purpose of this paper is by using the generalized forward–backward splitting method and implicit midpoint rule to propose an iterative algorithm for finding a common element of the set of solutions to a system of quasi variational inclusions with accretive mappings and the set of fixed points for a $$\lambda $$ -strict pseudo-contractive mapping in Banach spaces. Some strong convergence theorems of the sequence generated by the algorithm are proved. The results presented in the paper extend and improve some recent results. At the end of the paper, some applications to a system of variational inequalities problem, monotone variational inequalities, convex minimization problem and convexly constrained linear inverse problem are presented.