Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 598191, 10 pages
Approximate Proximal Point Algorithms for Finding Zeroes of Maximal Monotone Operators in Hilbert Spaces
1Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, South Korea
2Department of Mathematics and the RINS, Gyeongsang National University, Chinju 660-701, South Korea
3Department of Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, China
Received 1 March 2007; Accepted 27 November 2007
Academic Editor: H. Bevan Thompson
Copyright © 2008 Yeol Je Cho et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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
is regarded as an error
sequence such that . Let
be a real sequence such that
and . For any fixed , define a sequence
iteratively as for all .
Then converges strongly to a point as , where .