Shapiro's cyclic inequality for even n

被引：4

作者：

Bushell, PJ ^{[1
]}

McLeod, JB

机构：

[1] Univ Sussex, Sch Math Sci, Brighton BN1 9QH, E Sussex, England

[2] Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2002年 / 7卷 / 03期

关键词：

cyclic inequality; Shapiro's cyclic sum; Diananda result; tridiagonal matrix;

D O I：

10.1080/10255830290030426

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In 1954 H. S. Shapiro proposed an inequality for a cyclic sum in n variables. All the numerical evidence indicates that the inequality is true for even n less than or equal to 12 and for odd n less than or equal to 23. We give an analytic proof for the case n = 12, which implies the former result. The remaining case n = 23 remains an open problem.

引用

页码：331 / 348

页数：18