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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2026年4月3日

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

摘要

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.