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

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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Correspondence to JongSoo Jung.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Jung, J. Strong Convergence of Iterative Schemes for Zeros of Accretive Operators in Reflexive Banach Spaces. Fixed Point Theory Appl 2010, 103465 (2010). https://doi.org/10.1155/2010/103465

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Keywords

  • Banach Space
  • Differential Geometry
  • Convergence Theorem
  • Iteration Method
  • Strong Convergence