Relative convexity and its applications

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• 作者：Constantin P. Niculescu ; Ionel Roven?a
• 关键词：Primary 26B25 ; Secondary 26D15 ; Convex function ; Supporting hyperplane ; Positive measure ; Doubly stochastic matrix
• 刊名：Aequationes Mathematicae
• 出版年：2015
• 出版时间：October 2015
• 年：2015
• 卷：89
• 期：5
• 页码：1389-1400
• 全文大小：545 KB
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• 作者单位：Constantin P. Niculescu (1)
  Ionel Roven?a (1)
  
  1. Department of Mathematics, University of Craiova, 200585, Craiova, Romania
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  Combinatorics
  
• 出版者：Birkh盲user Basel
• ISSN：1420-8903

文摘

We discuss a rather general condition under which the inequality of Jensen works for certain convex combinations of points not all in the domain of convexity of the function under attention. Based on this fact, an extension of the Hardy–Littlewood–Pólya theorem of majorization is proved and a new insight is given into the problem of risk aversion in mathematical finance. Mathematics Subject Classification Primary 26B25 Secondary 26D15