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Continuous Selections, Collectively Fixed Points and Weak Knaster–Kuratowski–Mazurkiewicz Mappings in Optimization

Author

Listed:
  • P. Q. Khanh

    (International University of Hochiminh City)

  • V. S. T. Long

    (Cao Thang College of Technology)

  • N. H. Quan

    (University of Science of Hochiminh City)

Abstract

We prove theorems on continuous selections, collectively fixed points, collectively coincidence points, weak Knaster–Kuratowski–Mazurkiewicz mappings and provide their applications in various optimization-related problems. Each of our theorems is demonstrated by using its preceding assertions. The results contain and improve a number of existing ones in the recent literature. They are shown to be also more advantageous in applications in optimization.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:151:y:2011:i:3:d:10.1007_s10957-011-9889-0
    DOI: 10.1007/s10957-011-9889-0
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    References listed on IDEAS

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    1. 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.
    2. D. T. Luc, 2008. "An Abstract Problem in Variational Analysis," Journal of Optimization Theory and Applications, Springer, vol. 138(1), pages 65-76, July.
    3. Tarafdar, E., 1991. "A fixed point theorem and equilibrium point of an abstract economy," Journal of Mathematical Economics, Elsevier, vol. 20(2), pages 211-218.
    4. 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.
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