Popoviciu's inequality for functions of several variables

被引：11

作者：

Bencze, Mihaly ^{[1
]}

Niculescu, Constantin P. ^{[1
]}

Popovici, Florin ^{[2
]}

机构：

[1] Univ Craiova, Dept Math, RO-200585 Craiova, Romania

[2] Coll Grigore Moisil, Brasov, Romania

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2010年 / 365卷 / 01期

关键词：

Popoviciu's inequality; Choquet's theory; Convex function;

D O I：

10.1016/j.jmaa.2009.10.069

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

T. Popoviciu (1965) [13] has proved an interesting characterization of the convex functions of one real variable, based on an inequality relating the values at any three points x(1), x(2), x(3), with the values at their means of different orders: (x(1) + x(2))/2, (x(2) + x(3))/2, (x(3) + x(1))/2 and (x(1) + x(2) + x(3))/3. The aim of our paper is to develop a higher dimensional analogue of the usual convexity based on his characterization. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：399 / 409

页数：11

共 13 条

[1] The Hermite-Hadamard inequality on simplices [J].