Open Access

Approximate Proximal Point Algorithms for Finding Zeroes of Maximal Monotone Operators in Hilbert Spaces

Journal of Inequalities and Applications20072008:598191

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

Received: 1 March 2007

Accepted: 27 November 2007

Published: 4 December 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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Authors’ Affiliations

(1)
Department of Mathematics Education and the RINS, Gyeongsang National University
(2)
Department of Mathematics and the RINS, Gyeongsang National University
(3)
Department of Mathematics, Shijiazhuang Mechanical Engineering College

Copyright

© Yeol Je Cho et al. 2008

This article is published under license to BioMed Central Ltd. 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.