Necessary and sucient conditions for symmetric homogeneous polynomial inequalities of degree four and six in real variables
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Authors
Vasile Cirtoaje
- Department of Automatic Control and Computers, University of Ploiesti, Ploiesti, Romania.
Abstract
Let \(f_n(x; y; z)\) be a symmetric homogeneous polynomial of degree \(n = 4\) or \(n = 6\), in three real variables. We
give necessary and sufficient conditions to have \(f_n(x; y; z) \geq 0\) for all real numbers \(x; y; z\). Then, we apply
the obtained results to prove several relevant symmetric homogeneous polynomial inequalities of degree four
and six.
Share and Cite
ISRP Style
Vasile Cirtoaje, Necessary and sucient conditions for symmetric homogeneous polynomial inequalities of degree four and six in real variables, Journal of Nonlinear Sciences and Applications, 5 (2012), no. 5, 307--320
AMA Style
Cirtoaje Vasile, Necessary and sucient conditions for symmetric homogeneous polynomial inequalities of degree four and six in real variables. J. Nonlinear Sci. Appl. (2012); 5(5):307--320
Chicago/Turabian Style
Cirtoaje, Vasile. "Necessary and sucient conditions for symmetric homogeneous polynomial inequalities of degree four and six in real variables." Journal of Nonlinear Sciences and Applications, 5, no. 5 (2012): 307--320
Keywords
- Symmetric homogeneous polynomial
- necessary and sufficient conditions
- real variables.
MSC
References
-
[1]
T. Ando, Some Homogeneous Cyclic Inequalities of Three Variables of Degree Three and Four, Aust. J. Math. Anal. Appl., 7 (2010), 14 pages
-
[2]
V. Cirtoaje, On the Cyclic Homogeneous Polynomial Inequalities of Degree Four, Journal of Inequalities in Pure and Applied Mathematics, 10 (2009), 10 pages
-
[3]
V. Cirtoaje, Algebraic Inequalities , GIL Publishing House, (2006)
-
[4]
, Art of Problem Solving Forum, May, (2009),
-
[5]
, Art of Problem Solving Forum, August, (2009),
-
[6]
, Art of Problem Solving Forum, August, (2010),
-
[7]
, Art of Problem Solving Forum, July, (2009),
-
[8]
, Art of Problem Solving Forum, April, (2008),
-
[9]
, Art of Problem Solving Forum, March, (2008),
-
[10]
, Art of Problem Solving Forum, May, (2009),
-
[11]
, Art of Problem Solving Forum, February, (2008),