A Generalized Iterative Algorithm for Hierarchical Fixed Points Problems and Variational Inequalities - Vahid Dadashi (International Journal of Analysis and Applications, 2017)
In this paper we propose a method for approximating of the common fixed point in $\bigcap\limits_{n=1}^∞ F(T_n)$ where $\{T_n\}$ is a countable family of nonexpansive mappings on a closed convex subset $C$ of a real Hilbert space $\mathcal{H}$. Then, we prove strong convergence theorems with less control conditions for $\{T_n\}$ which solves some variational inequality. The main results improve and extend the corresponding results of "F. Cianciaruso, G. Marino, L. Muglia, and Y. Yao, On a two-step algorithm for hierarchical fixed point problems and variational inequalities, J. Inequal. Appl., 2009 (2009), Article ID 208692" and "Y. Yao, Y.J. Cho, and Y.C. Liou, Iterative algorithms for hierarchical fixed points problems and variational inequalities, Mathematical and Computer Modelling, 52(9) (2010), 1697--1705".