Journal
SYMMETRY-BASEL
Volume 12, Issue 4, Pages -Publisher
MDPI
DOI: 10.3390/sym12040503
Keywords
two-step extragradient method; strong convergence theorem; equilibrium problem; strongly pseudomonotone equilibrium problems; lipschitz-like conditions; Hilbert spaces
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Funding
- King Mongkut's University of Technology Thonburi through the `KMUTT 55th Anniversary Commemorative Fund'
- Theoretical and Computational Science (TaCS) Center under Computational and Applied Science for Smart research Innovation research Cluster (CLASSIC), Faculty of Science, KMUTT
- Petchra Pra Jom Doctoral Scholarship Academic [39/2560]
- Rajamangala University of Technology Thanyaburi (RMUTTT) [NSF62D0604]
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In this paper, we propose a new method, which is set up by incorporating an inertial step with the extragradient method for solving a strongly pseudomonotone equilibrium problems. This method had to comply with a strongly pseudomonotone property and a certain Lipschitz-type condition of a bifunction. A strong convergence result is provided under some mild conditions, and an iterative sequence is accomplished without previous knowledge of the Lipschitz-type constants of a cost bifunction. A sufficient explanation is that the method operates with a slow-moving stepsize sequence that converges to zero and non-summable. For numerical explanations, we analyze a well-known equilibrium model to support our well-established convergence result, and we can see that the proposed method seems to have a significant consistent improvement over the performance of the existing methods.
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