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A fixed point theorem for discontinuous functions

Author

Listed:
  • HERINGS, P. Jean-Jacques
  • van der LAAN, Gerard
  • TALMAN, Dolf
  • YANG, Zaifu

Abstract

Any function from a non-empty polytope into itself that is locally gross direction preserving is shown to have the fixed point property. Brouwer's fixed point theorem for continuous functions is a special case. We discuss the application of the result in the area of non-cooperative game theory. This discussion paper has resulted in a publication in Operations Research Letters . (2008, vol. 36, issue 1, pp.89-93.)
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • HERINGS, P. Jean-Jacques & van der LAAN, Gerard & TALMAN, Dolf & YANG, Zaifu, 2009. "A fixed point theorem for discontinuous functions," LIDAM Reprints CORE 2154, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:2154
    DOI: 10.1016/j.orl.2007.03.008
    Note: In : Operations Research Letters, 36, 89-93, 2008
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    Cited by:

    1. is not listed on IDEAS
    2. Zaifu Yang, 2008. "On the Solutions of Discrete Nonlinear Complementarity and Related Problems," Mathematics of Operations Research, INFORMS, vol. 33(4), pages 976-990, November.
    3. Philippe Bich, 2006. "Some fixed point theorems for discontinuous mappings," Cahiers de la Maison des Sciences Economiques b06066, Université Panthéon-Sorbonne (Paris 1).
    4. Philippe Bich, 2006. "Some fixed point theorems for discontinuous mappings," Post-Print halshs-00119033, HAL.
    5. Takao Fujimoto, 2013. "Fixed Point Theorems for Discontinuous Maps on a Non-convex Domain," Metroeconomica, Wiley Blackwell, vol. 64(3), pages 547-572, July.
    6. Philippe Bich, 2008. "An answer to a question of herings et al," Post-Print halshs-00287667, HAL.
    7. Philippe Bich, 2007. "Nash equilibrium existence for some discontinuous games," Post-Print halshs-00188764, HAL.
    8. Philippe Bich, 2008. "An answer to a question of herings et al," Working Papers halshs-00265464, HAL.
    9. Philippe Bich, 2008. "An answer to a question of herings et al," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00265464, HAL.

    More about this item

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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