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Open AccessFeature PaperArticle

The Inertial Sub-Gradient Extra-Gradient Method for a Class of Pseudo-Monotone Equilibrium Problems

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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
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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, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
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Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
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Program in Applied Statistics, Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi, Thanyaburi, Pathumthani 12110, Thailand
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Department of Mathematics, College of Science and Arts, King Abdulaziz University, P.O. Box 344, Rabigh 21911, Saudi Arabia
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Authors to whom correspondence should be addressed.
Symmetry 2020, 12(3), 463; https://doi.org/10.3390/sym12030463
Received: 16 January 2020 / Revised: 28 February 2020 / Accepted: 1 March 2020 / Published: 15 March 2020
(This article belongs to the Special Issue Symmetry in Nonlinear Functional Analysis and Optimization Theory)
In this article, we focus on improving the sub-gradient extra-gradient method to find a solution to the problems of pseudo-monotone equilibrium in a real Hilbert space. The weak convergence of our method is well-established based on the standard assumptions on a bifunction. We also present the application of our results that enable to solve numerically the pseudo-monotone and monotone variational inequality problems, in addition to the particular presumptions required by the operator. We have used various numerical examples to support our well-proved convergence results, and we can show that the proposed method involves a considerable influence over-running time and the total number of iterations. View Full-Text
Keywords: sub-gradient extra-gradient method; strongly pseudo-monotone equilibrium problems; convex quadratic optimization; strong convergence; Hilbert spaces sub-gradient extra-gradient method; strongly pseudo-monotone equilibrium problems; convex quadratic optimization; strong convergence; Hilbert spaces
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Rehman, H.; Kumam, P.; Kumam, W.; Shutaywi, M.; Jirakitpuwapat, W. The Inertial Sub-Gradient Extra-Gradient Method for a Class of Pseudo-Monotone Equilibrium Problems. Symmetry 2020, 12, 463.

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