This paper presents two inertial extragradient algorithms for finding a solution of split pseudomonotone equilibrium problems in the setting real Hilbert spaces. The weak and strong convergence theorems introduced are presented under some constraint qualifications scalar sequences. discussions on numerical experiments also provided to demonstrate effectiveness proposed algorithms.

We introduce a new iterative scheme for finding a common element of the set of solutions of the equilibrium problems, the set of solutions of variational inequality for a relaxed cocoercive mapping, and the set of fixed points of a nonexpansive mapping. The results presented in this paper extend and improve some recent results of Ceng and Yao 2008 , Yao 2007 , S. Takahashi andW. Takahashi 2007 ...