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

被引：14

作者：

Arfat, Yasir ^{[1
]}

Kumam, Poom ^{[1
,2
,3
]}

Ngiamsunthorn, Parinya Sa ^{[4
]}

Khan, Muhammad Aqeel Ahmad ^{[5
]}

Sarwar, Hammad ^{[5
]}

Fukhar-ud-Din, Hafiz ^{[6
]}

机构：

[1] King Mongkuts Univ Technol Thonburi KMUTT, KMUTTFixed Point Res Lab, KMUTT Fixed Point Theory & Applicat Res Grp, Dept Math,Fac Sci, 126 Pracha Uthit Rd, Bangkok 10140, Thailand

[2] King Mongkuts Univ Technol Thonburi KMUTT, Ctr Excellence Theoret & Computat Sci TaCS CoE, Sci Lab Bldg,126 Pracha Uthit Rd, Bangkok 10140, Thailand

[3] China Med Univ, China Med Univ Hosp, Dept Med Res, Taichung 40402, Taiwan

[4] King Mongkuts Univ Technol Thonburi KMUTT, Dept Math, Fac Sci, 126 Pracha Uthit Rd, Bangkok 10140, Thailand

[5] COMSATS Univ Islamabad, Dept Math, Lahore Campus, Lahore 54000, Pakistan

[6] Islamia Univ Bahawalpur, Dept Math, Baghdad Campus, Bahawalpur 63100, Pakistan

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2020年 / 2020卷 / 01期

关键词：

Extragradient method; Split equilibrium problem; Fixed point problem; Nonexpansive semigroup; Weak and strong convergence; 47H05; 47H09; 47J05; 49H05; STRONG-CONVERGENCE THEOREM; VARIATIONAL-INEQUALITIES; MAPPINGS; PROJECTION; SETS;

D O I：

10.1186/s13662-020-02956-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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.

引用

页数：21

共 50 条

[1] Approximation results for split equilibrium problems and fixed point problems of nonexpansive semigroup in Hilbert spaces
Yasir Arfat
Poom Kumam
Parinya Sa Ngiamsunthorn
Muhammad Aqeel Ahmad Khan
Hammad Sarwar
Hafiz Fukhar-ud-Din
[J]. Advances in Difference Equations, 2020
[2] An Iterative Method for Equilibrium, Variational Inequality, and Fixed Point Problems for a Nonexpansive Semigroup in Hilbert Spaces
Nguyen Thi Thu Thuy
[J]. Bulletin of the Malaysian Mathematical Sciences Society, 2015, 38 : 113 - 130
[3] An Iterative Method for Equilibrium, Variational Inequality, and Fixed Point Problems for a Nonexpansive Semigroup in Hilbert Spaces
Nguyen Thi Thu Thuy
[J]. BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2015, 38 (01) : 113 - 130
[4] Generalized equilibrium problems and fixed point problems for nonexpansive semigroups in Hilbert spaces
Uthai Kamraksa
Rabian Wangkeeree
[J]. Journal of Global Optimization, 2011, 51 : 689 - 714
[5] Generalized equilibrium problems and fixed point problems for nonexpansive semigroups in Hilbert spaces
Kamraksa, Uthai
Wangkeeree, Rabian
[J]. JOURNAL OF GLOBAL OPTIMIZATION, 2011, 51 (04) : 689 - 714
[6] ON SOLVING SPLIT EQUILIBRIUM PROBLEMS AND FIXED POINT PROBLEMS OF α-NONEXPANSIVE MULTI-VALUED MAPPINGS IN HILBERT SPACES
Li, Yang
Zhang, Congjun
Wang, Yuehu
[J]. FIXED POINT THEORY, 2023, 24 (02): : 641 - 660
[7] Shrinking projection methods for solving split equilibrium problems and fixed point problems for asymptotically nonexpansive mappings in Hilbert spaces
Witthayarat, Uamporn
Abdou, Afrah A. N.
Cho, Yeol Je
[J]. FIXED POINT THEORY AND APPLICATIONS, 2015, : 1 - 14
[8] Shrinking projection methods for solving split equilibrium problems and fixed point problems for asymptotically nonexpansive mappings in Hilbert spaces
Uamporn Witthayarat
Afrah A N Abdou
Yeol Je Cho
[J]. Fixed Point Theory and Applications, 2015
[9] SOME RESULTS FOR EQUILIBRIUM PROBLEMS AND FIXED POINT PROBLEMS IN HILBERT SPACES
Cho, Yeol Je
Qin, Xiaolong
Kang, Shin Min
[J]. JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, 2009, 11 (02) : 294 - 316
[10] SPLIT FIXED POINT PROBLEMS FOR QUASI-NONEXPANSIVE MAPPINGS IN HILBERT SPACES
Sharma, Shagun
Chandok, Sumit
[J]. UPB Scientific Bulletin, Series A: Applied Mathematics and Physics, 2024, 86 (01): : 109 - 118

← 1 2 3 4 5 →