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

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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.

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Authors and Affiliations

  1. Mathematics Department, Nanjing University, Nanjing, 210093, P.R. China

    Z. Y. Huang

  2. Mathematics Department, COMSATS Institute of Information Technology, Islamabad, Pakistan

    M. A. Noor

  3. Mathematics Department, College of Science, King Saud University, Riyadh, Saudi Arabia

    M. A. Noor & E. Al-Said

Authors
  1. Z. Y. Huang
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  2. M. A. Noor
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  3. E. Al-Said
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Corresponding author

Correspondence to M. A. Noor.

Additional information

Communicated by F. Giannessi.

The research of Prof. Z.Y. Huang is supported by NSFC (National Natural Science Foundation of China) Project grant 10871092.

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Huang, Z.Y., Noor, M.A. & Al-Said, E. On an Open Question of Takahashi for Nonexpansive Mappings and Inverse Strongly Monotone Mappings. J Optim Theory Appl 147, 194–204 (2010). https://doi.org/10.1007/s10957-010-9705-2

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  • DOI: https://doi.org/10.1007/s10957-010-9705-2

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