Approximate Proximal Point Algorithms for Finding Zeroes of Maximal Monotone Operators in Hilbert Spaces
© Yeol Je Cho et al. 2008
Received: 1 March 2007
Accepted: 27 November 2007
Published: 4 December 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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