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An approximation method for continuous pseudocontractive mappings
Journal of Inequalities and Applications volume 2006, Article number: 28950 (2006)
Let be a closed convex subset of a real Banach space, is continuous pseudocontractive mapping, and is a fixed-Lipschitzian strongly pseudocontractive mapping. For any, let be the unique fixed point of. We prove that if has a fixed point and has uniformly Gâteaux differentiable norm, such that every nonempty closed bounded convex subset of has the fixed point property for nonexpansive self-mappings, then converges to a fixed point of as approaches to 0. The results presented extend and improve the corresponding results of Morales and Jung (2000) and Hong-Kun Xu (2004).
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Song, Y., Chen, R. An approximation method for continuous pseudocontractive mappings. J Inequal Appl 2006, 28950 (2006). https://doi.org/10.1155/JIA/2006/28950
- Banach Space
- Approximation Method
- Convex Subset
- Real Banach Space
- Unique Fixed Point