A simple proof of Popoviciu's inequality

Journal of Numerical Analysis and Approximation Theory

卷:37

Mihaly Bencze¹  Florin Popovici² 

[1] Aprily Lajos College, Braşov;

[2] Grigore Moisil College, Braşov;

关键词: Popoviciu's inequality;    convex function;    convex combination;   

DOI  :  

来源: DOAJ

【 摘 要 】

T. Popoviciu [5] has proved in 1965 the following inequality relating the values of a convex function \(f:I\rightarrow\mathbb{R}\) at the weighted arithmetic means of the subfamilies of a given family of points \(x_{1},...,x_{n}\in I\):\begin{align*}& \sum\limits_{1\leq i_{1}<\cdots

【 授权许可】

Unknown