An inertial multi-step algorithm for solving equilibrium problems

In this paper, we introduce an algorithm based upon the proximal-point and inertial term extrapolation step for solving equilibrium problems in a real Hilbert space. The inertial term extrapolation step is introduced to speed up the rate of convergence of the iteration process. Under some appropriate assumptions on the bifunctions involving pseudomonotone and Lipschitz-type conditions, we obtain the weak convergence of the iterative sequence generated by the proposed algorithm. A numerical experiment of the algorithm is provided to illustrate the numerical behavior and also comparison with some other related algorithms in the literature. © 2020 Yokohama Publications. All rights reserved.