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Bibliographic Information
- Other Title
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- トツキョリ クウカン ニ オケル Berge ノ サイダイチ テイリ ノ ギャクモンダイ
- <Article>Inverse of the Berge Maximum Theorem in Convex Metric Spaces
- 論説
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Description
type:text
The Berge maximum theorem is a fundamental and important theorem in the general equilibrium theory of mathematical economics. Komiya studied an inverse problem of this theorem and obtained interesting results in finite dimensional spaces. Recently, Komiya's re- sult was extended to some infinite dimensional spaces. In this paper, we study an inverse of the Berge maximum theorem in some convex metric spaces, that is, we deal with the following problem : Let X be a metric space and let Y be a convex metric space. Let Γ : X-ο Y be a nonempty compact convex-valued upper semicontinuous multi-valued mapping. Then dose there exist a continuous function f : X × Y ⟶ R such that (i) Γ(x)={y ⋳ Y : f(x, y) = max_<z⋳y> f(x, z)} for any x⋳X ; (ii) f (x,・) is quasi-concave for any x⋳X? Our main result gives an affirmative answer to this problem.
source:Economic journal of Chiba University
Journal
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- 千葉大学経済研究 = Economic journal of Chiba University
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千葉大学経済研究 = Economic journal of Chiba University 17 (4), 595-606, 2003-03-12
千葉大学経済学会
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Details 詳細情報について
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- CRID
- 1050570022161863936
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- NII Article ID
- 110000465966
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- NII Book ID
- AN10005358
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- ISSN
- 09127216
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- NDL BIB ID
- 6573661
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- Text Lang
- ja
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- Article Type
- departmental bulletin paper
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- Data Source
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- IRDB
- NDL Search
- CiNii Articles