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On the Strong Convergence of Viscosity Approximation Process for Quasinonexpansive Mappings in Hilbert Spaces

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  • Kanokwan Wongchan
  • Satit Saejung

Abstract

We improve the viscosity approximation process for approximation of a fixed point of a quasi‐nonexpansive mapping in a Hilbert space proposed by Maingé (2010). An example beyond the scope of the previously known result is given.

Suggested Citation

  • Kanokwan Wongchan & Satit Saejung, 2011. "On the Strong Convergence of Viscosity Approximation Process for Quasinonexpansive Mappings in Hilbert Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    • Handle: RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:385843
    DOI: 10.1155/2011/385843
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    References listed on IDEAS

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    1. Filomena Cianciaruso & Giuseppe Marino & Luigi Muglia & Haiyun Zhou, 2008. "Strong Convergence of Viscosity Methods for Continuous Pseudocontractions in Banach Spaces," International Journal of Stochastic Analysis, Hindawi, vol. 2008, pages 1-11, December.
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    Cited by:

    1. Maingé, Paul-Emile, 2014. "A viscosity method with no spectral radius requirements for the split common fixed point problem," European Journal of Operational Research, Elsevier, vol. 235(1), pages 17-27.
    2. F. Cianciaruso & G. Marino & A. Rugiano & B. Scardamaglia, 2014. "On Strong Convergence of Halpern’s Method Using Averaged Type Mappings," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    3. Satit Saejung & Kanokwan Wongchan, 2013. "Strong Convergence for a Strongly Quasi‐Nonexpansive Sequence in Hilbert Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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