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

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...

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Bibliographic Details
Published in:Advances in difference equations 2020-09, Vol.2020 (1), p.1-21, Article 512
Main Authors: Arfat, Yasir, Kumam, Poom, Ngiamsunthorn, Parinya Sa, Khan, Muhammad Aqeel Ahmad, Sarwar, Hammad, Fukhar-ud-Din, Hafiz
Format: Article
Language:English
Subjects:
Analysis
Difference and Functional Equations
Extragradient method
Fixed point problem
Functional Analysis
Mathematics
Mathematics and Statistics
Nonexpansive semigroup
Ordinary Differential Equations
Partial Differential Equations
Split equilibrium problem
Weak and strong convergence
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Summary: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.
ISSN:1687-1847
1687-1847
DOI:10.1186/s13662-020-02956-8