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Convergence analysis of a general inertial projection-type method for solving pseudomonotone equilibrium problems with applications

Journal of Inequalities and Applications , Volume 2021, pp 1-27; doi:10.1186/s13660-021-02591-1

Abstract: In this paper, we introduce a new algorithm by incorporating an inertial term with a subgradient extragradient algorithm to solve the equilibrium problems involving a pseudomonotone and Lipschitz-type continuous bifunction in real Hilbert spaces. A weak convergence theorem is well established under certain mild conditions for the bifunction and the control parameters involved. Some of the applications to solve variational inequalities and fixed point problems are considered. Finally, several numerical experiments are performed to demonstrate the numerical efficacy and superiority of the proposed algorithm over other well-known existing algorithms.
Keywords: Pseudomonotone bifunction / Equilibrium problem / Weak convergence / Lipschitz-type conditions / Variational inequality problem

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