Abstract
In this paper, we suggest and analyze a relaxed viscosity iterative method for a commutative family of nonexpansive self-mappings defined on a nonempty closed convex subset of a reflexive Banach space. We prove that the sequence of approximate solutions generated by the proposed iterative algorithm converges strongly to a solution of a variational inequality. Our relaxed viscosity iterative method is an extension and variant form of the original viscosity iterative method. The results of this paper can be viewed as an improvement and generalization of the previously known results that have appeared in the literature.
| Original language | English |
|---|---|
| Pages (from-to) | 813-822 |
| Number of pages | 10 |
| Journal | Journal of Computational and Applied Mathematics |
| Volume | 230 |
| Issue number | 2 |
| DOIs | |
| State | Published - 15 Aug 2009 |
| Externally published | Yes |
Keywords
- Common fixed points
- Nonexpansive mapping
- Relaxed viscosity approximation method
- Strong convergence
- Uniformly Gâteaux differentiable norm
- Variational inequalities
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics
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