Approximation of common solutions of the infinite family of equilibrium problems in Banach Spaces

In this paper, we study convergence analysis of the sequence generated by extragradient method for an infinite family of the equilibrium problems in Banach spaces. We first prove weak convergence of the generated sequence to a common solution of the infinite family of the equilibrium problems. Then we use Halpern type regularization method in order to prove strong convergence of the generated sequence to a common equilibrium point.