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Approximate Proximal Point Algorithms for Finding Zeroes of Maximal Monotone Operators in Hilbert Spaces

Abstract

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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Correspondence to Haiyun Zhou.

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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

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Keywords

  • Hilbert Space
  • Monotone Operator
  • Full Article
  • Maximal Monotone
  • Maximal Monotone Operator
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