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

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.

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