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

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Abstract

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.

Journal

  • Okayama economics review

    Okayama economics review 31(3), 529-537, 1999-12

    岡山大学経済学会

Codes

  • NII Article ID (NAID)
    120002695983
  • NII NACSIS-CAT ID (NCID)
    AN00032897
  • Text Lang
    JPN
  • Article Type
    journal article
  • Journal Type
    大学紀要
  • ISSN
    03863069
  • NDL Article ID
    4938228
  • NDL Source Classification
    ZD11(経済--経済学)
  • NDL Call No.
    Z3-940
  • Data Source
    NDL  IR 
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