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Existence Results for General Inclusions Using Generalized KKM Theorems with Applications to Minimax Problems

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  • P. Q. Khanh

    (International University of Hochiminh City)

  • N. H. Quan

    (Information Technology College of Hochiminh City)

Abstract

Applying generalized KKM-type theorems established in our previous paper (Khanh et al. in Nonlinear Anal. 71:1227–1234, 2009), we prove the existence of solutions to a general variational inclusion problem, which contains most of the existing results of this type. As applications, we obtain minimax theorems in various settings and saddle-point theorems in particular. Examples are given to explain advantages of our results.

Suggested Citation

  • P. Q. Khanh & N. H. Quan, 2010. "Existence Results for General Inclusions Using Generalized KKM Theorems with Applications to Minimax Problems," Journal of Optimization Theory and Applications, Springer, vol. 146(3), pages 640-653, September.
    • Handle: RePEc:spr:joptap:v:146:y:2010:i:3:d:10.1007_s10957-010-9690-5
    DOI: 10.1007/s10957-010-9690-5
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    References listed on IDEAS

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    1. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(2), pages 427-429, April.
    2. Nguyen Hai & Phan Khanh & Nguyen Quan, 2009. "On the existence of solutions to quasivariational inclusion problems," Computational Optimization and Applications, Springer, vol. 45(4), pages 565-581, December.
    3. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(1), pages 223-229, February.
    4. P. Q. Khanh & L. M. Luu, 2004. "On the Existence of Solutions to Vector Quasivariational Inequalities and Quasicomplementarity Problems with Applications Break to Traffic Network Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 123(3), pages 533-548, December.
    5. L. J. Lin & W. P. Wan, 2004. "KKM Type Theorems and Coincidence Theorems with Applications to the Existence of Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 123(1), pages 105-122, October.
    6. G. M. Lee & S. H. Kum, 2000. "On Implicit Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 104(2), pages 409-425, February.
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    Cited by:

    1. P. Q. Khanh & N. H. Quan, 2011. "Generic Stability and Essential Components of Generalized KKM Points and Applications," Journal of Optimization Theory and Applications, Springer, vol. 148(3), pages 488-504, March.
    2. P. Q. Khanh & V. S. T. Long & N. H. Quan, 2011. "Continuous Selections, Collectively Fixed Points and Weak Knaster–Kuratowski–Mazurkiewicz Mappings in Optimization," Journal of Optimization Theory and Applications, Springer, vol. 151(3), pages 552-572, December.
    3. Phan Khanh & Vo Long, 2014. "Invariant-point theorems and existence of solutions to optimization-related problems," Journal of Global Optimization, Springer, vol. 58(3), pages 545-564, March.

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