Abstract
In this paper, we introduce an iterative scheme for finding common fixed point of an infinite family of non-expansive mappings in Hilbert space. Furthermore, we prove that the proposed iterative scheme converges strongly to a common fixed point. As an application, we succeed in applying our algorithm to find a solution of generalized mixed equilibrium problems systems. Our results improve and extend the corresponding results announced by W. Takahashi, Y. Takeuchi, R. Kubota (J. Math. Anal. Appl. 341: 276-286, 2008); S. Takahashi, W. Takahashi (Nonlinear Anal. 69: 1025-1033, 2008); N. Petrot, K. Wattanawitoon, P. Kumam (Nonlinear Anal. Hybrid Syst., 2010, doi:10.1016/j.nahs.2010.03.008) and some others in references.