Strong Convergence of Viscosity Iteration Methods for Nonexpansive Mappings
We propose a new viscosity iterative scheme for finding fixed points of nonexpansive mappings in a reflexive Banach space having a uniformly Gâteaux differentiable norm and satisfying that every weakly compact convex subset of the space has the fixed point property for nonexpansive mappings. Certain...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2009-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2009/573156 |
| Summary: | We propose a new viscosity iterative scheme for finding fixed points of nonexpansive mappings
in a reflexive Banach space having a uniformly Gâteaux differentiable norm and satisfying that every weakly compact convex subset of the space has the fixed point property for nonexpansive mappings. Certain different control conditions for viscosity iterative scheme are given and strong convergence of viscosity iterative
scheme to a solution of a ceratin variational inequality is established. |
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| ISSN: | 1085-3375 1687-0409 |