Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 103465, 19 pages
doi:10.1155/2010/103465
Research Article

Strong Convergence of Iterative Schemes for Zeros of Accretive Operators in Reflexive Banach Spaces

Jong Soo Jung

Department of Mathematics, Dong-A University, Busan 604-714, South Korea

Received 6 August 2009; Accepted 11 January 2010

Academic Editor: Anthony To Ming Lau

Copyright © 2010 Jong Soo Jung. 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 introduce composite iterative schemes by the viscosity iteration method for finding a zero of an accretive operator in reflexive Banach spaces. Then, under certain differen control conditions, we establish strong convergence theorems on the composite iterative schemes. The main theorems improve and develop the recent corresponding results of Aoyama et al. (2007), Chen and Zhu (2006, 2008), Jung (2010), Kim and Xu (2005), Qin and Su (2007) and Xu (2006) as well as Benavides et al. (2003), Kamimura and Takahashi (2000), Maingé (2006), and Nakajo (2006).