- Research Article
- Open access
- Published:
An Implicit Hierarchical Fixed-Point Approach to General Variational Inequalities in Hilbert Spaces
Fixed Point Theory and Applications volume 2011, Article number: 748918 (2011)
Abstract
Let be a nonempty closed convex subset of a real Hilbert space . Let be a -Lipschitzian and -strongly monotone operator with constants , be nonexpansive mappings with where denotes the fixed-point set of , and be a -contraction with coefficient . Let and , where . For each , let be a unique solution of the fixed-point equation . We derive the following conclusions on the behavior of the net along the curve : (i) if , as , then strongly, which is the unique solution of the variational inequality of finding such that and (ii) if , as , then strongly, which is the unique solution of some hierarchical variational inequality problem.
Publisher note
To access the full article, please see PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Zeng, L., Wen, CF. & Yao, J. An Implicit Hierarchical Fixed-Point Approach to General Variational Inequalities in Hilbert Spaces. Fixed Point Theory Appl 2011, 748918 (2011). https://doi.org/10.1155/2011/748918
Received:
Accepted:
Published:
DOI: https://doi.org/10.1155/2011/748918