Paper Title:

Necessary and Sufficient Conditions for Cyclic Homogeneous Polynomial Inequalities of Degree Four in Real Variables

Author(s):

Vasile Cirtoaje and Yuanzhe Zhou

Department of Automatic Control and Computers
University of Ploiesti
Romania.
vcirtoaje@upg-ploiesti.ro.
 

High School Affiliated to Wuhan University, China

Abstract:

In this paper, we give two sets of necessary and sufficient conditions that the inequality f₄(x,y,z) ≥ 0 holds for any real numbers x,y,z, where f₄(x,y,z) is a cyclic homogeneous polynomial of degree four. In addition, all equality cases of this inequality are analysed. For the particular case in which f₄(1,1,1)=0, we get the main result in [3]. Several applications are given to show the effectiveness of the proposed methods.

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