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

Volume 6, Issue 2, pp 74--85
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### Authors

Yuanzhe Zhou - The School of Physics and Technology at Wuhan University, China. Vasile Cirtoaje - Department of Automatic Control and Computers, University of Ploiesti, Ploiesti, Romania.

### Abstract

We establish some strong sufficient conditions that the inequality $f_4(x; y; z) \geq 0$ 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 $f_4(x; y; z) \geq 0$ does not hold for all real numbers $x; y; z$, we conjecture that the proposed sufficient conditions are also necessary that$f_4(x; y; z) \geq 0$ for all nonnegative real numbers $x; y; z$. Several applications are given to show the effectiveness of the proposed methods.

### Share and Cite

##### ISRP Style

Yuanzhe Zhou, Vasile Cirtoaje, Some strong sufficient conditions for cyclic homogeneous polynomial inequalities of degree four in nonnegative variables, Journal of Nonlinear Sciences and Applications, 6 (2013), no. 2, 74--85

##### AMA Style

Zhou Yuanzhe, Cirtoaje Vasile, Some strong sufficient conditions for cyclic homogeneous polynomial inequalities of degree four in nonnegative variables. J. Nonlinear Sci. Appl. (2013); 6(2):74--85

##### Chicago/Turabian Style

Zhou, Yuanzhe, Cirtoaje, Vasile. "Some strong sufficient conditions for cyclic homogeneous polynomial inequalities of degree four in nonnegative variables." Journal of Nonlinear Sciences and Applications, 6, no. 2 (2013): 74--85

### Keywords

• Cyclic homogeneous polynomial
• strong sufficient conditions
• necessary and sufficient conditions
• nonnegative real variables.

•  26D05

### References

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