A Strong Method for Symmetric Homogeneous Polynomial Inequalities of Degree Six in Nonnegative Real Variables

Vasile Cirtoaje

doi:10.9734/BJMCS/2014/7062

Research Article Open access CC BY 3.0

A Strong Method for Symmetric Homogeneous Polynomial Inequalities of Degree Six in Nonnegative Real Variables

Vasile Cirtoaje

Journal of Advances in Mathematics and Computer Science · pp. 685–703 · Published 5 Dec 2013

10.9734/BJMCS/2014/7062

Abstract

Let f6(x, y, z) be a symmetric homogeneous polynomial of degree six. Based on cancelling the high coefficient of f6(x, y, z), we give some practical sufficient conditions to have f6(x, y, z) ≥ 0 for any nonnegative real variables x, y, z. Some applications are given in order to emphasize the effectiveness of the proposed method.

Symmetric homogeneous inequality Sixth degree polynomial Sufficient conditions Highest coefficient Nonnegative real variables.

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Vasile Cirtoaje (2013). A Strong Method for Symmetric Homogeneous Polynomial Inequalities of Degree Six in Nonnegative Real Variables. Journal of Advances in Mathematics and Computer Science , 685–703. https://doi.org/10.9734/BJMCS/2014/7062

Affiliations

Vasile Cirtoaje — Department of Automatic Control and Computers, University of Ploiesti, Bdul Bucuresti, 39, Ploiesti, Romania.

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