A Characterization of Cone-Convexity for Set-Valued Functions by Cone-Quasiconvexity

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• 作者：Daishi Kuroiwa ; Nicolae Popovici ; Matteo Rocca
• 关键词：Set ; valued affine function ; Cone ; convexity ; Cone ; quasiconvexity ; R氓dstr枚m鈥檚 cancellation law ; 26B25 ; 46A40 ; 54C60
• 刊名：Set-Valued and Variational Analysis
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：23
• 期：2
• 页码：295-304
• 全文大小：191 KB
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• 作者单位：Daishi Kuroiwa (1)
  Nicolae Popovici (2)
  Matteo Rocca (3)
  
  1. Department of Mathematics and Computer Sciences, Shimane University, Matsue, 690-8504, Japan
  2. Faculty of Mathematics and Computer Science, Babe艧-Bolyai University of Cluj-Napoca, 400084, Cluj-Napoca, Romania
  3. Department of Economics, University of Insubria, 21100, Varese, Italy
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  Geometry
  
• 出版者：Springer Netherlands
• ISSN：1877-0541

文摘

A classical result by Crouzeix (1977) states that a real-valued function is convex if and only if any function obtained from it by adding a linear functional is quasiconvex. The principal aim of this paper is to present a similar characterization for certain cone-convex set-valued functions by means of cone-quasiconvex and affine set-valued functions.