“…Yamada's method is subsequently extended and modified to solve more complex problems, containing finite or infinite nonexpansive mappings (see, e.g., [3,6,40] and references therein). In [40], based on the Yamada result, Zeng and Yao introduced an implicit method that converges weakly to a solution of a variational inequality, involving a Lipschitz continuous and strongly monotone mapping in a Hilbert space H, where the feasible set is that of common fixed points of a finite family of nonexpansive mappings on H. In [7], Ceng et al extended this result from nonexpansive mappings to Lipschitz pseudocontractive mappings and strictly pseudocontractive mappings on H. Recently, in [4], Buong and Anh proposed a strongly convergent implicit method, which is a modification of Yamada's result. In the case where the feasible set is that of common fixed points of an infinite family of nonexpansive mappings on H, based on the W-mapping (see [29]) and Moudafi's viscosity approximation method (see [23]), in [16,17], Kikkawa and Takahashi studied an implicit iteration scheme that converges strongly to a solution of the stated problem.…”