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Some Algorithms for Finding Fixed Points and Solutions of Variational Inequalities

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  • Jong Soo Jung

Abstract

We introduce new implicit and explicit algorithms for finding the fixed point of a k‐strictly pseudocontractive mapping and for solving variational inequalities related to the Lipschitzian and strongly monotone operator in Hilbert spaces. We establish results on the strong convergence of the sequences generated by the proposed algorithms to a fixed point of a k‐strictly pseudocontractive mapping. Such a point is also a solution of a variational inequality defined on the set of fixed points. As direct consequences, we obtain the unique minimum‐norm fixed point of a k‐strictly pseudocontractive mapping.

Suggested Citation

  • Jong Soo Jung, 2012. "Some Algorithms for Finding Fixed Points and Solutions of Variational Inequalities," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:153456
    DOI: 10.1155/2012/153456
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    References listed on IDEAS

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    1. Yonghong Yao & Muhammad Aslam Noor & Yeong-Cheng Liou, 2012. "Strong Convergence of a Modified Extragradient Method to the Minimum-Norm Solution of Variational Inequalities," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-9, December.
    2. Muhammad Aslam Noor & Khalida Inayat Noor & Zhenyu Huang & Eisa Al-Said, 2012. "Implicit Schemes for Solving Extended General Nonconvex Variational Inequalities," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    3. Yonghong Yao & Muhammad Aslam Noor & Yeong-Cheng Liou & Shin Min Kang, 2012. "Iterative Algorithms for General Multivalued Variational Inequalities," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    4. Yonghong Yao & Muhammad Aslam Noor & Yeong-Cheng Liou, 2012. "Strong Convergence of a Modified Extragradient Method to the Minimum‐Norm Solution of Variational Inequalities," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    5. Yonghong Yao & Muhammad Aslam Noor & Yeong-Cheng Liou & Shin Min Kang, 2012. "Iterative Algorithms for General Multivalued Variational Inequalities," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-10, December.
    6. Muhammad Aslam Noor & Khalida Inayat Noor & Zhenyu Huang & Eisa Al-Said, 2012. "Implicit Schemes for Solving Extended General Nonconvex Variational Inequalities," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-10, January.
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