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Gap function and global error bounds for generalized mixed quasi variational inequalities

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  • Khan, Suhel Ahmad
  • Chen, Jia-wei

Abstract

In this paper, we obtain some gap functions for generalized mixed quasi variational inequality problems in terms of regularized gap function and D-gap function. Further, by using these gap functions we obtain global error bounds for the solution of generalized mixed quasi variational inequality problems in Hilbert spaces. The results obtained in this paper generalize and improve some corresponding known results in literatures.

Suggested Citation

  • Khan, Suhel Ahmad & Chen, Jia-wei, 2015. "Gap function and global error bounds for generalized mixed quasi variational inequalities," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 71-81.
    • Handle: RePEc:eee:apmaco:v:260:y:2015:i:c:p:71-81
    DOI: 10.1016/j.amc.2015.03.056
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    References listed on IDEAS

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    1. J. Li & G. Mastroeni, 2010. "Vector Variational Inequalities Involving Set-valued Mappings via Scalarization with Applications to Error Bounds for Gap Functions," Journal of Optimization Theory and Applications, Springer, vol. 145(2), pages 355-372, May.
    2. D. Aussel & R. Correa & M. Marechal, 2011. "Gap Functions for Quasivariational Inequalities and Generalized Nash Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 151(3), pages 474-488, December.
    3. Rachana Gupta & Aparna Mehra, 2012. "Gap functions and error bounds for quasi variational inequalities," Journal of Global Optimization, Springer, vol. 53(4), pages 737-748, August.
    4. X. P. Ding, 2010. "Auxiliary Principle and Algorithm for Mixed Equilibrium Problems and Bilevel Mixed Equilibrium Problems in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 146(2), pages 347-357, August.
    5. D. Aussel & J. Dutta, 2011. "On Gap Functions for Multivalued Stampacchia Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 149(3), pages 513-527, June.
    Full references (including those not matched with items on IDEAS)

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