Another refinement of the Pólya–Szegö inequality

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Abstract

In this paper, the authors make use of certain analytical techniques for nonlinear algebraic equation systems in order to give another refinement of the Pólya–Szegö inequality in a triangle, which is associated with one of Chen’s theorems (see Chen (1993) [12] and Chen (2000) [13]). Some remarks and observations, as well as two closely-related open problems, are also presented.

Keywords

Pólya–Szegö inequality in a triangle
Best constant
Chen’s theorems
Sylvester’s resultant
Discriminant sequence
Nonlinear algebraic equation systems
Computer softwares Bottema and Maple (Version 9.0)
Pólya–Szegö inequality in a tetrahedron
Weitzenböck’s inequality

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