We introduce a new implicit iterative scheme with perturbation for finding the approximate solutions of a hierarchical variational inequality, that is, a variational inequality over the common fixed point set of a finite family of nonexpansive mappings. We establish some convergence theorems for the sequence generated by the proposed implicit iterative scheme. In particular, necessary and sufficient conditions for the strong convergence of the sequence are obtained.
"Implicit Iterative Method for Hierarchical Variational Inequalities." J. Appl. Math. 2012 (SI03) 1 - 14, 2012. https://doi.org/10.1155/2012/472935