A Generalized Iterative Algorithm for Hierarchical Fixed Points Problems and Variational Inequalities

Dadashi, Vahid; Amjadi, Somayeh

Research Article

A Generalized Iterative Algorithm for Hierarchical Fixed Points Problems and Variational Inequalities

Vahid Dadashi¹*
Somayeh Amjadi¹

‎Department of Mathematics‎, Sari Branch‎, ‎Islamic Azad University, ‎Sari‎, ‎Iran

* Corresponding author

Abstract

In this paper we propose a method for approximating of the common fixed point in $\bigcap\limits_{n=1}^\infty F(T_n)$ 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".

How to Cite

V. Dadashi, S. Amjadi, A Generalized Iterative Algorithm for Hierarchical Fixed Points Problems and Variational Inequalities, Int. J. Anal. Appl. 13 (2017), 54–63.

BibTeX

@article{Dadashi2017,
  author  = {Dadashi, Vahid and Amjadi, Somayeh},
  title   = {A Generalized Iterative Algorithm for Hierarchical Fixed Points Problems and Variational Inequalities},
  journal = {Int. J. Anal. Appl.},
  volume  = {13},
  year    = {2017},
  pages   = {54--63},
  doi     = {}
}

References

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