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Convergence on Composite Iterative Schemes for Nonexpansive Mappings in Banach Spaces
Fixed Point Theory and Applications volume 2008, Article number: 167535 (2008)
Let be a reflexive Banach space with a uniformly Gâteaux differentiable norm. Suppose that every weakly compact convex subset of has the fixed point property for nonexpansive mappings. Let be a nonempty closed convex subset of , a contractive mapping (or a weakly contractive mapping), and nonexpansive mapping with the fixed point set . Let be generated by a new composite iterative scheme: , , . It is proved that converges strongly to a point in , which is a solution of certain variational inequality provided that the sequence satisfies and , for some and the sequence is asymptotically regular.
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Jung, J.S. Convergence on Composite Iterative Schemes for Nonexpansive Mappings in Banach Spaces. Fixed Point Theory Appl 2008, 167535 (2008). https://doi.org/10.1155/2008/167535
- Banach Space
- Differential Geometry
- Nonexpansive Mapping
- Iterative Scheme
- Computational Biology