Explicit Halpern-type iterative algorithm for solving equilibrium problems with applications

A number of iterative algorithms have been established to solve equilibrium problems, and one of the most effective methods is a two-step extragradient method. The main objective of this study is to introduce a modified algorithm that is constructed around two methods; Halpern-type method and extragradient method with a new size rule to solve the equilibrium problems accompanied with pseudo-monotone and Lipschitz-type continuous bi-function in a real Hilbert space. Using certain mild conditions on the bi-function, as well as certain conditions on the iterative control parameters, proves a strong convergence theorem. The proposed algorithm uses a monotonic step size rule depending on local bi-function information. The main results are also used to solve variational inequalities and fixed-point problems. The numerical behavior of the proposed algorithm on different test problems is provided compared to other existing algorithms.