The ‘core’ of symmetric homogeneous polynomial inequalities of degree four of three real variables

Published in: Quaestiones Mathematicae
Volume 40, issue 8, 2017 , pages: 1135–1143
DOI: 10.2989/16073606.2017.1368731
Author(s): Mariyan MilevDepartment of Mathematics and Physics, Bulgaria, Nedelcho MilevDepartment of Mathematical Analysis, Bulgaria
Keywords: 26D05, 26D05


In this paper we explore inequalities between symmetric homogeneous polynomials of degree four of three real variables and three nonnegative real variables. The main theorems describe the cases in which the smallest possible coefficient is not expressed by the other coefficients. The problem is resolved by introducing a parametric representation.

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