An inertially constructed forward–backward splitting algorithm in Hilbert spaces - Arfat, Yasir; Kumam, Poom; Khan, Muhammad Aqeel Ahmad; Ngiamsunthorn, Parinya Sa; Kaewkhao, Attapol (Advances in difference equations, 2021)
In this paper, we develop an iterative algorithm whose architecture comprises a modified version of the forward–backward splitting algorithm and the hybrid shrinking projection algorithm. We provide theoretical results concerning weak and strong convergence of the proposed algorithm towards a common solution of the fixed point problem associated to a finite family of demicontractive operators, the split equilibrium problem and the monotone inclusion problem in Hilbert spaces. Moreover, we compute a numerical experiment to show the efficiency of the proposed algorithm. As a consequence, our results improve various existing results in the current literature.