# A modified extra-gradient method for a family of strongly pseudomonotone equilibrium problems in real Hilbert spaces

Volume 22, Issue 1, pp 38--48
Publication Date: June 05, 2020 Submission Date: March 19, 2020 Revision Date: April 10, 2020 Accteptance Date: April 27, 2020
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### Authors

Habib ur Rehman - KMUTTFixed Point Research Laboratory, KMUTT-Fixed Point Theory and Applications Research Group, SCL 802 Fixed Point Laboratory, Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand. Nuttapol Pakkaranang - KMUTTFixed Point Research Laboratory, KMUTT-Fixed Point Theory and Applications Research Group, SCL 802 Fixed Point Laboratory, Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand. Azhar Hussain - Department of Mathematics, University of Sargodha, Sargodha-40100, Pakistan. Nopparat Wairojjana - Applied Mathematics Program, Faculty of Science and Technology, Valaya Alongkorn Rajabhat University under the Royal Patronage (VRU), 1 Moo 20 Phaholyothin Road, Klong Neung, Klong Luang, Pathumthani, 13180, Thailand.

### Abstract

In this paper, we propose a modified extragradient method for solving a strongly pseudomonotone equilibrium problem in a real Hilbert space. A strong convergence theorem relative to our proposed method is proved and the proposed method has worked without having the information of a strongly pseudomonotone constant and the Lipschitz-type constants of a bifunction. We have carried out our numerical explanations to justify our well-established convergence results, and we can see that our proposed method has a substantial improvement over the time of execution and number iterations.

### Share and Cite

##### ISRP Style

Habib ur Rehman, Nuttapol Pakkaranang, Azhar Hussain, Nopparat Wairojjana, A modified extra-gradient method for a family of strongly pseudomonotone equilibrium problems in real Hilbert spaces, Journal of Mathematics and Computer Science, 22 (2021), no. 1, 38--48

##### AMA Style

Rehman Habib ur, Pakkaranang Nuttapol, Hussain Azhar, Wairojjana Nopparat, A modified extra-gradient method for a family of strongly pseudomonotone equilibrium problems in real Hilbert spaces. J Math Comput SCI-JM. (2021); 22(1):38--48

##### Chicago/Turabian Style

Rehman, Habib ur, Pakkaranang, Nuttapol, Hussain, Azhar, Wairojjana, Nopparat. "A modified extra-gradient method for a family of strongly pseudomonotone equilibrium problems in real Hilbert spaces." Journal of Mathematics and Computer Science, 22, no. 1 (2021): 38--48

### Keywords

• Equilibrium problem
• strongly pseudomonotone bifunction
• strong convergence theorem
• Lipschitz-type conditions
• variational inequality problems

•  47J25
•  47H09
•  47H06
•  47J05

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