Abstract
In this paper, we suggest and analyze a new extragradient iterative method, which is suggested by combining a modified extragradient method with the viscosity approximation method, for finding the common element of the set of fixed points of a countable family of nonexpansive mappings, and the solution set of the variational inequality in a Hilbert space. This new method includes the extragradient and viscosity methods as special cases. We also consider the strong convergence of the proposed method under some mild conditions. Several special cases are also discussed. Results proved in this paper may be viewed as an improvement and refinement of the previously known results.