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Hartman–Stampacchia Theorems, Gale–Nikaidô–Debreu Lemma, and Brouwer and Kakutani Fixed-Point Theorems

Author

Listed:
  • Pascal Gourdel

    (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Cuong Le Van

    (IPAG Business School, CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Ngoc-Sang Pham

    (EM Normandie - École de Management de Normandie = EM Normandie Business School)

  • Cuong Tran Viet

    (TIMAS - Institute of Mathematics and Applied Science, Thang Long University)

Abstract

This paper uses the Hartman–Stampacchia theorems as the primary tool to prove the Gale–Nikaidô–Debreu lemmas. It also establishes a cycle of equivalences among the Hartman–Stampacchia theorems, the Gale–Nikaidô–Debreu lemmas, and Kakutani and Brouwer fixed-point theorems.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Pascal Gourdel & Cuong Le Van & Ngoc-Sang Pham & Cuong Tran Viet, 2026. "Hartman–Stampacchia Theorems, Gale–Nikaidô–Debreu Lemma, and Brouwer and Kakutani Fixed-Point Theorems," Post-Print hal-05588633, HAL.
    • Handle: RePEc:hal:journl:hal-05588633
    DOI: 10.1007/s10957-026-02971-x
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    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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