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On an Open Question of Takahashi for Nonexpansive Mappings and Inverse Strongly Monotone Mappings

Author

Listed:
  • Z. Y. Huang

    (Nanjing University)

  • M. A. Noor

    (COMSATS Institute of Information Technology
    King Saud University)

  • E. Al-Said

    (King Saud University)

Abstract

In this paper, we suggest and analyze an iteration method studied by Takahashi and Toyoda (J. Optim. Theory Appl. 118(2):417–428, 2003) for finding a common element of a set of fixed points of nonexpansive mappings and a set of solutions of variational inequalities with inverse strongly monotone mappings under some mild conditions. The strong convergence is proved and positive answer is given to an open question posed by Takahashi and Toyoda.

Suggested Citation

  • Z. Y. Huang & M. A. Noor & E. Al-Said, 2010. "On an Open Question of Takahashi for Nonexpansive Mappings and Inverse Strongly Monotone Mappings," Journal of Optimization Theory and Applications, Springer, vol. 147(1), pages 194-204, October.
    • Handle: RePEc:spr:joptap:v:147:y:2010:i:1:d:10.1007_s10957-010-9705-2
    DOI: 10.1007/s10957-010-9705-2
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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.
    2. N. Nadezhkina & W. Takahashi, 2006. "Weak Convergence Theorem by an Extragradient Method for Nonexpansive Mappings and Monotone Mappings," Journal of Optimization Theory and Applications, Springer, vol. 128(1), pages 191-201, January.
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    Cited by:

    1. Z. Y. Huang & M. A. Noor, 2012. "Studies on Common Solutions of a Variational Inequality and a Fixed-Point Problem," Journal of Optimization Theory and Applications, Springer, vol. 154(2), pages 525-535, August.

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