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Iterative Algorithms for General Multivalued Variational Inequalities

Author

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

Abstract

We introduce and study some new classes of variational inequalities and the Wiener‐Hopf equations. Using essentially the projection technique, we establish the equivalence between these problems. This equivalence is used to suggest and analyze some iterative methods for solving the general multivalued variational in equalities in conjunction with nonexpansive mappings. We prove a strong convergence result for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the general multivalued variational inequalities under some mild conditions. Several special cases are also discussed.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:768272
    DOI: 10.1155/2012/768272
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    References listed on IDEAS

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    1. Patrick Jaillet & Damien Lamberton & Bernard Lapeyre, 1990. "Variational inequalities and the pricing of American options," Post-Print hal-01667008, HAL.
    2. M. A. Noor & E. A. Al-Said, 1999. "Wiener–Hopf Equations Technique for Quasimonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 103(3), pages 705-714, December.
    3. 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. Muhammad Aslam Noor & Khalida Inayat Noor & Saira Zainab & Eisa Al-Said, 2012. "Regularized Mixed Variational‐Like Inequalities," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. 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).
    3. M. De la Sen, 2013. "Some Results on Fixed and Best Proximity Points of Precyclic Self‐Mappings," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    4. 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).
    5. 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).
    6. Muhammad Aslam Noor, 2012. "Some Aspects of Extended General Variational Inequalities," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    7. M. De la Sen & E. Karapinar, 2013. "Best Proximity Points of Generalized Semicyclic Impulsive Self‐Mappings: Applications to Impulsive Differential and Difference Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    8. 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).
    9. 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).
    10. 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).
    11. M. De la Sen, 2013. "Some Results on Fixed and Best Proximity Points of Multivalued Cyclic Self‐Mappings with a Partial Order," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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