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Some Aspects of Extended General Variational Inequalities

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  • Muhammad Aslam Noor

Abstract

Noor (“Extended general variational inequalities,” 2009, “Auxiliary principle technique for extended general variational inequalities,” 2008, “Sensitivity analysis of extended general variational inequalities,” 2009, “Projection iterative methods for extended general variational inequalities,” 2010) introduced and studied a new class of variational inequalities, which is called the extended general variational inequality involving three different operators. This class of variational inequalities includes several classes of variational inequalities and optimization problems. The main motivation of this paper is to review some aspects of these variational inequalities including the iterative methods and sensitivity analysis. We expect that this paper may stimulate future research in this field along with novel applications.

Suggested Citation

  • Muhammad Aslam Noor, 2012. "Some Aspects of Extended General Variational Inequalities," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:303569
    DOI: 10.1155/2012/303569
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    References listed on IDEAS

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    1. 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).
    2. Muhammad Aslam Noor & Khalida Inayat Noor & Eisa Al-Said, 2012. "On New Proximal Point Methods for Solving the Variational Inequalities," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-7, November.
    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. Muhammad Aslam Noor & Khalida Inayat Noor & Eisa Al-Said, 2012. "On New Proximal Point Methods for Solving the Variational Inequalities," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    5. E. A. Youness, 1999. "E-Convex Sets, E-Convex Functions, and E-Convex Programming," Journal of Optimization Theory and Applications, Springer, vol. 102(2), pages 439-450, August.
    6. 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.
    7. 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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    Citations

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    Cited by:

    1. Moosaei, H. & Ketabchi, S. & Noor, M.A. & Iqbal, J. & Hooshyarbakhsh, V., 2015. "Some techniques for solving absolute value equations," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 696-705.
    2. Muhammad Aslam Noor & Khalida Inayat Noor, 2012. "Explicit Iterative Method for Variational Inequalities on Hadamard Manifolds," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    3. Muhammad Aslam Noor, 2012. "Parametric Extended General Mixed Variational Inequalities," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(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. Rudong Chen, 2012. "Iterative Schemes for Fixed Point Computation of Nonexpansive Mappings," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    6. Muhammad Aslam Noor & Khalida Inayat Noor, 2012. "Existence Results for General Mixed Quasivariational Inequalities," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    7. Pavlo O. Kasyanov & Luisa Toscano & Nina V. Zadoianchuk, 2012. "Long‐Time Behaviour of Solutions for Autonomous Evolution Hemivariational Inequality with Multidimensional “Reaction‐Displacement” Law," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    8. Muhammad Aslam Noor & Khalida Inayat Noor, 2012. "Some New Classes of Extended General Mixed Quasi‐Variational Inequalities," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    9. Shunhou Fan & Shin Min Kang & Muhammad Aslam Noor & Yonghong Yao, 2012. "Modified Noor′s Extragradient Method for Solving Generalized Variational Inequalities in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    10. 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).
    11. Yeong-Cheng Liou, 2012. "Computing the Fixed Points of Strictly Pseudocontractive Mappings by the Implicit and Explicit Iterations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    12. Yiran He, 2012. "The Tikhonov Regularization Method for Set‐Valued Variational Inequalities," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).

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