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

Advances in Difference Equations

article

Arfat, Yasir¹  Kumam, Poom¹  Ngiamsunthorn, Parinya Sa⁴  Khan, Muhammad Aqeel Ahmad⁵  Sarwar, Hammad⁵  Fukhar-ud-Din, Hafiz⁶ 

[1] 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);Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, King Mongkut’s University of Technology Thonburi (KMUTT);Department of Medical Research, China Medical University Hospital, China Medical University;Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT);Department of Mathematics, COMSATS University Islamabad;Department of Mathematics, The Islamia University of Bahawalpur

关键词: Extragradient method;    Split equilibrium problem;    Fixed point problem;    Nonexpansive semigroup;    Weak and strong convergence;   

DOI  :  10.1186/s13662-020-02956-8

学科分类：航空航天科学

来源: SpringerOpen

【 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