Closed convex sets of Minkowski type

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:444

Article

Martinez-Legaz, J. E.^1,2  Pintea, Cornel³ 

[1] Univ Autonoma Barcelona, Dept Econ & Econ Hist, E-08193 Barcelona, Spain

[2] Barcelona Grad Sch Math BGSMath, Barcelona, Spain

[3] Univ Babes Bolyai, Fac Math & Comp Sci, Cluj Napoca, Romania

关键词: Closed convex sets;    Extreme points;   

DOI  :  10.1016/j.jmaa.2016.06.073

来源: Elsevier

【 摘 要 】

In this paper we provide several characterizations of Minkowski sets, i.e. closed, possibly unbounded, convex sets which are representable as the convex hulls of their sets of extreme points. The equality between the relative boundary of a closed convex set containing no lines and its Pareto-like associated set ensures the Minkowski property of the set. In two dimensions this equality characterizes the Minkowski sets containing no lines. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free