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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