Another refinement of the Pólya–Szegö inequality

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.