Strong convergence of a forward–backward splitting method with a new step size for solving monotone inclusions

Abstract

In this paper, our interest is in investigating the monotone inclusion problems in the framework of real Hilbert spaces. To solve this problem, we propose a new modified forward–backward splitting method using the viscosity method (Moudafi in J Math Anal Appl 241(527):46–55, 2000). Under some mild conditions, we establish the strong convergence of the iterative sequence generated by the proposed algorithm. The advantage of our algorithm is that it does not require the co-coercivity of the single-valued operator. Our result improves related results in the literature. Finally, the performances of our proposed method are presented through numerical experiments in signal recovery.