A family of extragradient methods for solving equilibrium problems

In this paper we introduce a class of numerical methods for solving an equilibrium problem. This class depends on a parameter and contains the classical extragradient method and a generalization of the two-step extragradient method proposed recently by Zykina and Melen'chuk for solving variational inequality problems. Convergence of each algorithm of this class to a solution of the equilibrium problem is obtained under the condition that the equilibrium function associated with the problem is pseudomonotone and Lipschitz continuous. Some preliminary numerical results are given to compare the numerical behavior of the two-step extragradient method with respect to the other methods of the class and in particular to the extragradient method.