Journal of Advances in Mathematics and Computer Science

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

Vasile Cirtoaje *

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

*Author to whom correspondence should be addressed.

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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.

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

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