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Hartman-Stampacchia theorem, Gale-Nikaido-Debreu lemma, and Brouwer and Kakutani fixed-point theorems

Author

Listed:
  • Gourdel, Pascal
  • Le Van, Cuong
  • Pham, Ngoc-Sang
  • Tran Viet, Cuong

Abstract

This paper uses the Hartman-Stampacchia theorems as primary tool to prove the Gale-Nikaido-Debreu lemma. It also establishes a full equivalence circle among the Hartman Stampacchia theorems, the Gale-Nikaido-Debreu lemmas, and Kakutani and Brouwer fixed point theorems.

Suggested Citation

  • Gourdel, Pascal & Le Van, Cuong & Pham, Ngoc-Sang & Tran Viet, Cuong, 2023. "Hartman-Stampacchia theorem, Gale-Nikaido-Debreu lemma, and Brouwer and Kakutani fixed-point theorems," MPRA Paper 116541, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:116541
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    References listed on IDEAS

    as
    1. Quah, John K.-H., 2008. "The existence of equilibrium when excess demand obeys the weak axiom," Journal of Mathematical Economics, Elsevier, vol. 44(3-4), pages 337-343, February.
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    More about this item

    Keywords

    Hartman-Stampacchia theorem; Gale-Nikaido-Debreu Lemma; Brouwer fixed points theorem; Kakutani fixed points theorem.;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium

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