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New extragradient methods with non-convex combination for pseudomonotone equilibrium problems with applications in Hilbert spaces

Wang Shenghua (Department of Mathematics and Physics, North China Electric Power University, Baoding, China)
Zhang Yifan (Department of Mathematics and Physics, North China Electric Power University, Baoding, China)
Ping Ping (Dean’s Offce, North China Electric Power University, Baoding, China)
Cho Yeol Je (Department of Mathematics Education, Gyeongsang National University, Jinju, Korea + Center for General Education, China Medical University, Taichung, Taiwan)
Guo Haichao (Department of Electrical Engineering, North China Electric Power University, Baoding, China)

In the literature, the most authors modify the viscosity methods or hybrid projection methods to construct the strong convergence algorithms for solving the pseudomonotone equilibrium problems. In this paper, we introduce some new extragradient methods with non-convex combination to solve the pseudomonotone equilibrium problems in Hilbert space and prove the strong convergence for the constructed algorithms. Our algorithms are very different with the existing ones in the literatures. As the application, the fixed point theorems for strict pseudo-contraction are considered. Finally, some numerical examples are given to show the effectiveness of the algorithms.

Keywords: Equilibrium problem, pseudomonotone equilibrium problem, fixed point, Hilbert space