Approximation results for split equilibrium problems and fixed point problems of nonexpansive semigroup in Hilbert spaces

Advances in Difference Equations

Hammad Sarwar¹  Muhammad Aqeel Ahmad Khan¹  Parinya Sa Ngiamsunthorn²  Hafiz Fukhar-ud-Din³  Yasir Arfat⁴  Poom Kumam⁵ 

[1] Department of Mathematics, COMSATS University Islamabad, Lahore Campus, 54000, Lahore, Pakistan;Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road,Band Mod, Thrung Khru, 10140, Bangkok, Thailand;Department of Mathematics, The Islamia University of Bahawalpur, Baghdad Campus, 63100, Bahawalpur, Pakistan;KMUTTFixed Point Research Laboratory, KMUTT-Fixed Point Theory and Applications Research Group, Department of Mathematics, Faculity of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, 10140, Bangkok, Thailand;KMUTTFixed Point Research Laboratory, KMUTT-Fixed Point Theory and Applications Research Group, Department of Mathematics, Faculity of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung 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,Band Mod,Thrung Khru, 10140, Bangkok, Thailand;Department of Medical Research, China Medical University Hospital, China Medical University, 40402, Taichung, Taiwan;

关键词: Extragradient method;    Split equilibrium problem;    Fixed point problem;    Nonexpansive semigroup;    Weak and strong convergence;    47H05;    47H09;    47J05;    49H05;   

DOI  :  10.1186/s13662-020-02956-8

来源: Springer

【 摘 要 】

In this paper, we study a modified extragradient method for computing a common solution to the split equilibrium problem and fixed point problem of a nonexpansive semigroup in real Hilbert spaces. The weak and strong convergence characteristics of the proposed algorithm are investigated by employing suitable control conditions in such a setting of spaces. As a consequence, we provide a simplified analysis of various existing results concerning the extragradient method in the current literature. We also provide a numerical example to strengthen the theoretical results and the applicability of the proposed algorithm.

【 授权许可】

CC BY