The Australian Journal of Mathematical Analysis and Applications

@inproceedings{Zhou2012TheAJ,
  title={The Australian Journal of Mathematical Analysis and Applications},
  author={Yuanzhe Zhou},
  year={2012}
}
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.