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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)
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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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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DOI: https://doi.org/10.1155/2008/598191