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