Strongly convex set-valued maps

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• 作者：Hugo Leiva ; Nelson Merentes ; Kazimierz Nikodem…
• 关键词：Strongly convex function ; Strongly convex set ; valued map ; Strongly convex set ; Primary 26B25 ; Secondary 54C60 ; 46C15 ; 39B62
• 刊名：Journal of Global Optimization
• 出版年：2013
• 出版时间：November 2013
• 年：2013
• 卷：57
• 期：3
• 页码：695-705
• 全文大小：183KB
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• 作者单位：Hugo Leiva (1)
  Nelson Merentes (2)
  Kazimierz Nikodem (3)
  José Luis Sánchez (2)
  
  1. Departamento de Matemáticas, Facultad de Ciencias, Universidad de los Andes, Mérida, Venezuela
  2. Escuela de Matemáticas, Universidad Central de Venezuela, Caracas, Venezuela
  3. Department of Mathematics and Computer Science, University of Bielsko-Bia?a, ul. Willowa 2, 43-309, Bielsko-Bia?a, Poland
  
• ISSN：1573-2916

文摘

We introduce the notion of strongly $t$ -convex set-valued maps and present some properties of it. In particular, a Bernstein–Doetsch and Sierpiński-type theorems for strongly midconvex set-valued maps, as well as a Kuhn-type result are obtained. A representation of strongly $t$ -convex set-valued maps in inner product spaces and a characterization of inner product spaces involving this representation is given. Finally, a connection between strongly convex set-valued maps and strongly convex sets is presented.