An inertially constructed forward–backward splitting algorithm in Hilbert spaces

被引：0
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作者：
Yasir Arfat
Poom Kumam
Muhammad Aqeel Ahmad Khan
Parinya Sa Ngiamsunthorn
Attapol Kaewkhao
机构：
[1] King Mongkut’s University of Technology Thonburi (KMUTT),KMUTT Fixed Point Research Laboratory, KMUTT
[2] King Mongkut’s University of Technology Thonburi (KMUTT),Fixed Point Theory and Applications Research Group, Department of Mathematics, Faculty of Science
[3] China Medical University,Center of Excellence in Theoretical and Computational Science (TaCS
[4] COMSATS University Islamabad,CoE), Science Laboratory Building
[5] King Mongkut’s University of Technology Thonburi (KMUTT),Department of Medical Research, China Medical University Hospital
[6] Chiang Mai University,Department of Mathematics
来源：
Advances in Difference Equations | / 2021卷
关键词：
Fixed point problem; Forward–backward splitting algorithm; Monotone inclusion problem; Split equilibrium problem; Demicontractive operator; Hilbert spaces; 90C25; 47H05; 47H10; 65K05;
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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.
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