Some strong sufficient conditions for cyclic homogeneous polynomial inequalities of degree four in nonnegative variables

被引：1

作者：

Zhou, Yuanzhe ^{[1
]}

Cirtoaje, Vasile ^{[2
]}

机构：

[1] Wuhan Univ, Sch Phys & Technol, Wuhan, Peoples R China

[2] Univ Ploiesti, Dept Automat Control & Comp, Ploiesti, Romania

来源：

JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS | 2013年 / 6卷 / 02期

关键词：

Cyclic homogeneous polynomial; strong sufficient conditions; necessary and sufficient conditions; nonnegative real variables;

D O I：

10.22436/jnsa.006.02.03

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish some strong sufficient conditions that the inequality f(4)(x, y, z) >= 0 holds for all nonnegative real numbers x, y, z, where f(4)(x, y, z) is a cyclic homogeneous polynomial of degree four. In addition, In the case f(4)(1,1,1) = 0 and also in the case when the inequality f(4)(x, y, z) >= 0 does not hold for all real numbers x, y, z, we conjecture that the proposed sufficient conditions are also necessary that f(4)(x, y, z) >= 0 for all nonnegative real numbers x, y, z. Several applications are given to show the effectiveness of the proposed methods.

引用

页码：74 / 85

页数：12