不等式体系における Tuckerの定理の非線型への一般化 Nonlinear Generalizations of Tucker's Theorem on Inequality Systems

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This note is to prove Tucker's theorem on linear inequalities based on the proof method of minimax theorems which uses Kakutani's fixed point theorem. One device is necessary to convert the minimax theorems to Tucker's formulation. This is a slight restriction on the image sets when creating a set-valued map. We also present nonlinear generalizations of Tucker's theorem employing the same method. All we need is that the set of variable values for which an objective function attains its maximum is convex. This objective function is a convex combination of functions. We also present a proof of the fact that a local characterization of inequality systems, when a given mapping is differentiable, can be made global provided the mapping is concave.

収録刊行物

  • 岡山大学経済学会雑誌

    岡山大学経済学会雑誌 31(3), 529-537, 1999-12

    岡山大学経済学会

各種コード

  • NII論文ID(NAID)
    120002695983
  • NII書誌ID(NCID)
    AN00032897
  • 本文言語コード
    JPN
  • 資料種別
    journal article
  • 雑誌種別
    大学紀要
  • ISSN
    03863069
  • NDL 記事登録ID
    4938228
  • NDL 雑誌分類
    ZD11(経済--経済学)
  • NDL 請求記号
    Z3-940
  • データ提供元
    NDL  IR 
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