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Existence Results for Vector Mixed Quasi-Complementarity Problems

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  • Suhel Ahmad Khan
  • Naeem Ahmad

Abstract

We introduce strong vector mixed quasi-complementarity problems and the corresponding strong vector mixed quasi-variational inequality problems. We establish equivalence between strong mixed quasi-complementarity problems and strong mixed quasi-variational inequality problem in Banach spaces. Further, using KKM-Fan lemma, we prove the existence of solutions of these problems, under pseudomonotonicity assumption. The results presented in this paper are extensions and improvements of some earlier and recent results in the literature.

Suggested Citation

  • Suhel Ahmad Khan & Naeem Ahmad, 2013. "Existence Results for Vector Mixed Quasi-Complementarity Problems," Journal of Mathematics, Hindawi, vol. 2013, pages 1-6, February.
    • Handle: RePEc:hin:jjmath:204348
    DOI: 10.1155/2013/204348
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    References listed on IDEAS

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    1. K. R. Kazmi & S. A. Khan, 2009. "Existence of Solutions to a Generalized System," Journal of Optimization Theory and Applications, Springer, vol. 142(2), pages 355-361, August.
    2. C. E. Lemke, 1965. "Bimatrix Equilibrium Points and Mathematical Programming," Management Science, INFORMS, vol. 11(7), pages 681-689, May.
    3. Suhel Khan, 2011. "Generalized vector implicit quasi complementarity problems," Journal of Global Optimization, Springer, vol. 49(4), pages 695-705, April.
    4. Huang, N.J. & Yang, X.Q. & Chan, W.K., 2007. "Vector complementarity problems with a variable ordering relation," European Journal of Operational Research, Elsevier, vol. 176(1), pages 15-26, January.
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    Cited by:

    1. Farhat Suhel & S. K. Srivastava & Suhel Ahmad Khan, 2014. "A Wiener-Hopf Dynamical System for Mixed Equilibrium Problems," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2014, pages 1-8, April.

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