Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 240450, 11 pages
doi:10.1155/2010/240450
Research Article

Strong and Weak Convergence of the Modified Proximal Point Algorithms in Hilbert Space

Xinkuan Chai,1 Bo Li,2 and Yisheng Song1

1College of Mathematics and Information Science, Henan Normal University, XinXiang 453007, China
2School of Mathematics and Statistics, AnYang Normal University, AnYang 455000, China

Received 26 October 2009; Revised 25 November 2009; Accepted 10 December 2009

Academic Editor: Tomonari Suzuki

Copyright © 2010 Xinkuan Chai 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.

Abstract

For a monotone operator T, we shall show weak convergence of Rockafellar's proximal point algorithm to some zero of T and strong convergence of the perturbed version of Rockafellar's to PZu under some relaxed conditions, where PZ is the metric projection from H onto Z=T−10. Moreover, our proof techniques are simpler than some existed results.