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Approximation of Fixed Points of Nonexpansive Mappings and Solutions of Variational Inequalities
Journal of Inequalities and Applications volume 2008, Article number: 284345 (2007)
Let be a real -uniformly smooth Banach space with constant , . Let and be a nonexpansive map and an -strongly accretive map which is also -Lipschitzian, respectively. Let be a real sequence in that satisfies the following condition: and . For and , define a sequence iteratively in by , , . Then, converges strongly to the unique solution of the variational inequality problem (search for such that for all , where . A convergence theorem related to finite family of nonexpansive maps is also proved.
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Chidume, C.E., Chidume, C.O. & Ali, B. Approximation of Fixed Points of Nonexpansive Mappings and Solutions of Variational Inequalities. J Inequal Appl 2008, 284345 (2007). https://doi.org/10.1155/2008/284345
- Variational Inequality
- Nonexpansive Mapping
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