Jensen-type geometric shapes

被引：2
|
作者：
Pasteczka, Pawel [1 ]
机构：
[1] Pedag Univ Krakow, Dept Math, Krakow, Poland
来源：
ANNALES UNIVERSITATIS PAEDAGOGICAE CRACOVIENSIS-STUDIA MATHEMATICA | 2020年 / 19卷 / 01期
关键词：
Shapes; Platonic shapes; sphere; ball; Jensen's inequality;
D O I：
10.2478/aupcsm-2020-0002
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We present both necessary and sufficient conditions for a convex closed shape such that for every convex function the average integral over the shape does not exceed the average integral over its boundary. It is proved that this inequality holds for n-dimensional parallelotopes, n-dimensional balls, and convex polytopes having the inscribed sphere (tangent to all its facets) with the centre in the centre of mass of its boundary.
引用
收藏
页码：27 / 33
页数：7
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