Abstract and Applied Analysis
Volume 2009 (2009), Article ID 795432, 20 pages
doi:10.1155/2009/795432
Research Article

Strong and Weak Convergence of Modified Mann Iteration for New Resolvents of Maximal Monotone Operators in Banach Spaces

Somyot Plubtieng and Wanna Sriprad

Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand

Received 18 January 2009; Accepted 2 June 2009

Academic Editor: Norimichi Hirano

Copyright © 2009 Somyot Plubtieng and Wanna Sriprad. 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

We prove strong and weak convergence theorems for a new resolvent of maximal monotone operators in a Banach space and give an estimate of the convergence rate of the algorithm. Finally, we apply our convergence theorem to the convex minimization problem. The result present in this paper extend and improve the corresponding result of Ibaraki and Takahashi (2007), and Kim and Xu (2005).