Abstract
In this paper, we consider a triple hierarchical variational inequalities (in short, THVI) with a finite family of nonexpansive mappings. By combining the viscosity approximation method, hybrid steepest-descent method and Mann’s iteration method, we propose the hybrid steepest-descent viscosity approximation method for solving the THVI. The strong convergence of this method to a unique solution of the THVI is studied. Under some mild conditions, a strong convergence result (to the unique solution of THVI) for another iterative algorithm is also presented.
| Original language | English |
|---|---|
| Pages (from-to) | 237-260 |
| Number of pages | 24 |
| Journal | Fixed Point Theory |
| Volume | 16 |
| Issue number | 2 |
| State | Published - 2015 |
Bibliographical note
Publisher Copyright:© 2015, House of the Book of Science. All rights reserved.
Keywords
- Fixed point
- Hybrid steepest-descent viscosity approximation method
- Monotone operators
- Nonexpansive mappings
- Strong convergence theorem
- Triple hierarchical variational inequalities
ASJC Scopus subject areas
- Analysis
- Computational Mathematics
- Applied Mathematics
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