Fixed Point Theory and Applications

, 2010:103465 | Cite as

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

Open Access
Research Article
Part of the following topical collections:
  1. Takahashi's Legacy in Fixed Point Theory

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).

Keywords

Banach Space Differential Geometry Convergence Theorem Iteration Method Strong Convergence 

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Copyright information

© Jong Soo Jung. 2010

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.

Authors and Affiliations

  1. 1.Department of MathematicsDong-A UniversityBusanSouth Korea

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