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Ishikawa’s Iterative Algorithm of Nonexpansive Mappings and Averaged Mappings

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Proceedings of the 2012 International Conference on Communication, Electronics and Automation Engineering

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 181))

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Abstract

In this paper we introduce and study Ishikawa’s iterative algorithm of nonexpansive mapping and averaged mappings in the setting of real Hilbert spaces. The main results presented in this paper extend the classic result of convergence of Mann’s iterative algorithm for nonexpansive mappings in the setting of Hilbert space and we prove the weak converge theorems.

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References

  1. Ishikawa, S.: Fixed point and iteration of a nonexpansive mapping in a Banach spaces. Proc. Amer. Math. Soc. 73, 65–71 (1976)

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Author information

Authors and Affiliations

  1. Department of Mathematic, Chengdu University of Information Technology, 610225, Chengdu, P.R. China

    Duan Qibin, Wang Erli, Wu Dingping & Xie Xuping

Authors
  1. Duan Qibin
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  2. Wang Erli
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  3. Wu Dingping
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  4. Xie Xuping
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Editor information

Editors and Affiliations

  1. Department of Engineering Technology, Missouri Western State University, Downs Drive 4525, 64507, St. Joseph, USA

    George Yang

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Qibin, D., Erli, W., Dingping, W., Xuping, X. (2013). Ishikawa’s Iterative Algorithm of Nonexpansive Mappings and Averaged Mappings. In: Yang, G. (eds) Proceedings of the 2012 International Conference on Communication, Electronics and Automation Engineering. Advances in Intelligent Systems and Computing, vol 181. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31698-2_97

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  • DOI: https://doi.org/10.1007/978-3-642-31698-2_97

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31697-5

  • Online ISBN: 978-3-642-31698-2

  • eBook Packages: EngineeringEngineering (R0)

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