The Australian Journal of Mathematical Analysis and Applications

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ISSN 1449-5910  


Paper Information

Paper Title:

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


Vasile Cirtoaje and Yuanzhe Zhou

Department of Automatic Control and Computers
University of Ploiesti

High School Affiliated to Wuhan University, China



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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