Forward–Backward Splitting Method for Solving a System of Quasi-Variational Inclusions

Abstract

The purpose of this paper is by using a generalized forward–backward splitting method 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 $$\lambda $$ -strictly 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. As applications, we utilize our results to study the approximation problem of solutions to a system of variational inequalities, accretive variational inequality problem and convex minimization problem in Banach spaces.