Approximate Proximal Point Algorithms for Finding Zeroes of Maximal Monotone Operators in Hilbert Spaces - Kang ShinMin (Journal of Inequalities and Applications, 2008)
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 .