GENERALIZED BARYCENTRIC COORDINATES AND JENSEN TYPE INEQUALITIES ON CONVEX POLYTOPES

被引:0
作者
Guessab, Allal [1 ]
机构
[1] Univ Pau & Pays Adour, CNRS, UMR 4152, Lab Math & Leurs Applicat, F-64000 Pau, France
关键词
Convex functions; Jensen's inequality; barycentric coordinates; Farkas' lemma; partitions of unity; supporting hyperplane;
D O I
暂无
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper we obtain some direct and converse new multidimensional Jensen's type inequalities on convex polytopes. Among the inequalities presented, we offer, as a particular case of our general results, a direct and converse multivariate extension of Mercer inequality. The main results are obtained with the help of the generalized barycentric coordinates. For deriving such inequalities, we will also establish, analyze, and discuss links between barycentric coordinates and certain class of partitions of unity. This method also allows us to derive continuous versions of various discrete inequalities established in our recent paper [7].
引用
收藏
页码:527 / 547
页数:21
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