We introduce a new iterative scheme that converges strongly to a common fixed point of a countable family of nonexpansive mappings in a Hilbert space such that the common fixed point is a solution of a hierarchical fixed point problem. Our results extend the ones of Moudafi, Xu, Cianciaruso et al., and Yao et al.
Gendai Gu. Shenghua Wang. Yeol Je Cho. "Strong Convergence Algorithms for Hierarchical Fixed Points Problems and Variational Inequalities." J. Appl. Math. 2011 1 - 17, 2011. https://doi.org/10.1155/2011/164978