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Strong Convergence of a Modified Extragradient Method to the Minimum‐Norm Solution of Variational Inequalities

Author

Listed:
  • Yonghong Yao
  • Muhammad Aslam Noor
  • Yeong-Cheng Liou

Abstract

We suggest and analyze a modified extragradient method for solving variational inequalities, which is convergent strongly to the minimum‐norm solution of some variational inequality in an infinite‐dimensional Hilbert space.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:817436
    DOI: 10.1155/2012/817436
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    References listed on IDEAS

    as
    1. Jen-Chih Yao, 1994. "Variational Inequalities with Generalized Monotone Operators," Mathematics of Operations Research, INFORMS, vol. 19(3), pages 691-705, August.
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    Cited by:

    1. 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).
    2. Shunhou Fan & Yonghong Yao, 2012. "Strong Convergence of a Projected Gradient Method," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    3. Yuanheng Wang & Weifeng Xuan, 2013. "Convergence Theorems for Common Fixed Points of a Finite Family of Relatively Nonexpansive Mappings in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. Muhammad Aslam Noor & Khalida Inayat Noor, 2012. "Proximal Point Methods for Solving Mixed Variational Inequalities on the Hadamard Manifolds," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    5. Peixia Yang & Yonghong Yao & Yeong-Cheng Liou & Rudong Chen, 2012. "Hybrid Algorithms of Nonexpansive Semigroups for Variational Inequalities," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    6. Xionghua Wu & Yeong-Cheng Liou & Zhitao Wu & Pei-Xia Yang, 2012. "Viscosity Methods of Asymptotically Pseudocontractive and Asymptotically Nonexpansive Mappings for Variational Inequalities," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    7. Yuanheng Wang, 2012. "Strong Convergence Theorems for Asymptotically Weak G‐Pseudo‐Ψ‐Contractive Non‐Self‐Mappings with the Generalized Projection in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    8. Muhammad Aslam Noor & Saira Zainab & Yonghong Yao, 2012. "Implicit Methods for Equilibrium Problems on Hadamard Manifolds," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    9. Youli Yu & Pei-Xia Yang & Khalida Inayat Noor, 2012. "Projection Algorithms for Variational Inclusions," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    10. Yeong-Cheng Liou & Yonghong Yao & Chun-Wei Tseng & Hui-To Lin & Pei-Xia Yang, 2012. "Iterative Algorithms Approach to Variational Inequalities and Fixed Point Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    11. Chaichana Jaiboon & Poom Kumam, 2012. "Viscosity Approximation Method for System of Variational Inclusions Problems and Fixed‐Point Problems of a Countable Family of Nonexpansive Mappings," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    12. Yaqin Zheng & Jinwei Shi, 2012. "New Iterative Manner Involving Sunny Nonexpansive Retractions for Pseudocontractive Mappings," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    13. Pongsakorn Sunthrayuth & Poom Kumam, 2013. "A New Computational Technique for Common Solutions between Systems of Generalized Mixed Equilibrium and Fixed Point Problems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    14. Rabian Wangkeeree & Pakkapon Preechasilp, 2012. "New Generalized Mixed Equilibrium Problem with Respect to Relaxed Semi‐Monotone Mappings in Banach Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).

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