A Modified Inertial Subgradient Extragradient Method for Solving Pseudomonotone Equilibrium Problem

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In this paper, we introduce and study a new modified inertial subgradient extragradient method that includes a self-adaptive step size and viscosity technique for approximating the solution of pseudomonotone equilibrium and fixed point problems in the framework of real Hilbert space. We obtain a strong convergence result of the proposed method under mild conditions. Furthermore, we apply our results to solve variational inequality. Finally, we present some numerical experiments for our proposed method in comparison with existing methods in the literature. Our result improves, extends and generalizes several existing results in the literature.

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