This article is part of the series Takahashi's Legacy in Fixed Point Theory.

Open Access Research Article

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

JongSoo Jung

Author Affiliations

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

Fixed Point Theory and Applications 2010, 2010:103465 doi:10.1155/2010/103465


The electronic version of this article is the complete one and can be found online at: http://www.fixedpointtheoryandapplications.com/content/2010/1/103465


Received:6 August 2009
Accepted:11 January 2010
Published:16 February 2010

© 2010 The Author(s).

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).

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