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Strong Convergence of an Iterative Scheme by a New Type of Projection Method for a Family of Quasinonexpansive Mappings

Author

Listed:
  • Y. Kimura

    (Tokyo Institute of Technology)

  • W. Takahashi

    (Tokyo Institute of Technology
    National Sun Yat-sen University)

  • J. C. Yao

    (National Sun Yat-sen University)

Abstract

We deal with a common fixed point problem for a family of quasinonexpansive mappings defined on a Hilbert space with a certain closedness assumption and obtain strongly convergent iterative sequences to a solution to this problem. We propose a new type of iterative scheme for this problem. A feature of this scheme is that we do not use any projections, which in general creates some difficulties in practical calculation of the iterative sequence. We also prove a strong convergence theorem by the shrinking projection method for a family of such mappings. These results can be applied to common zero point problems for families of monotone operators.

Suggested Citation

  • Y. Kimura & W. Takahashi & J. C. Yao, 2011. "Strong Convergence of an Iterative Scheme by a New Type of Projection Method for a Family of Quasinonexpansive Mappings," Journal of Optimization Theory and Applications, Springer, vol. 149(2), pages 239-253, May.
    • Handle: RePEc:spr:joptap:v:149:y:2011:i:2:d:10.1007_s10957-010-9788-9
    DOI: 10.1007/s10957-010-9788-9
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    References listed on IDEAS

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    1. W. Takahashi & M. Toyoda, 2003. "Weak Convergence Theorems for Nonexpansive Mappings and Monotone Mappings," Journal of Optimization Theory and Applications, Springer, vol. 118(2), pages 417-428, August.
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