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Approximate Proximal Point Algorithms for Finding Zeroes of Maximal Monotone Operators in Hilbert Spaces
Journal of Inequalities and Applications volume 2008, Article number: 598191 (2007)
Let be a real Hilbert space, a nonempty closed convex subset of , and a maximal monotone operator with . Let be the metric projection of onto . Suppose that, for any given , , and , there exists satisfying the following set-valued mapping equation: for all , where with as and is regarded as an error sequence such that . Let be a real sequence such that as and . For any fixed , define a sequence iteratively as for all . Then converges strongly to a point as , where .
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Cho, Y.J., Kang, S.M. & Zhou, H. Approximate Proximal Point Algorithms for Finding Zeroes of Maximal Monotone Operators in Hilbert Spaces. J Inequal Appl 2008, 598191 (2007). https://doi.org/10.1155/2008/598191
- Hilbert Space
- Monotone Operator
- Full Article
- Maximal Monotone
- Maximal Monotone Operator