An Iterative Approximation Method for a Countable Family of Nonexpansive Mappings in Hilbert Spaces

In this paper, to find a common element of the fixed point set of common fixed points of a countable family of nonexpansive mappings and the solution set of the variational inequality for a-inverse-strongly monotone, we introdnce an iterative approximation method in a real Hilbert space. Then the strong convergence theorem is proved under some appropriate conditions imposed on the parameters. This result extended and improved the corresponding results of Yao and Yao [15] and many others.