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Studies on Common Solutions of a Variational Inequality and a Fixed-Point Problem

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  • Z. Y. Huang

    (Nanjing University)

  • M. A. Noor

    (COMSATS Institute of Information Technology)

Abstract

In this paper, we construct a new projection method and prove the strong convergence for finding a common element of a set of fixed points of strict pseudo-contractions and a set of solutions of a variational inequality with inverse strongly monotone mappings in the setting of real Hilbert spaces. Our results improve and extend the recent results by Huang, Noor, and Al-Said (J. Optim. Theory Appl. 147(1):194–204, 2010), Takahashi and Toyoda (J. Optim. Theory Appl. 118(2):417–428, 2003).

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:154:y:2012:i:2:d:10.1007_s10957-012-0010-0
    DOI: 10.1007/s10957-012-0010-0
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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. 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.
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