An inertially constructed forward–backward splitting algorithm in Hilbert spaces

Advances in Difference Equations

Parinya Sa Ngiamsunthorn¹  Muhammad Aqeel Ahmad Khan²  Yasir Arfat³  Poom Kumam⁴  Attapol Kaewkhao⁵ 

[1] Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, 10140, Bangkok, Thailand;Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, 10140, Bangkok, Thailand;Department of Mathematics, COMSATS University Islamabad, Lahore Campus, 54000, Lahore, Pakistan;KMUTT Fixed Point Research Laboratory, KMUTT-Fixed Point Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, 10140, Bangkok, Thailand;KMUTT Fixed Point Research Laboratory, KMUTT-Fixed Point Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, 10140, Bangkok, Thailand;Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, 10140, Bangkok, Thailand;Department of Medical Research, China Medical University Hospital, China Medical University, 40402, Taichung, Taiwan;Research Center in Mathematics and Applied Mathematics, Faculty of Science, Chiang Mai University, 50200, Chiang Mai, Thailand;

关键词: Fixed point problem;    Forward–backward splitting algorithm;    Monotone inclusion problem;    Split equilibrium problem;    Demicontractive operator;    Hilbert spaces;    90C25;    47H05;    47H10;    65K05;   

DOI  :  10.1186/s13662-021-03277-0

来源: Springer

【 摘 要 】

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.

【 授权许可】

CC BY