Minkowski-type inequalities involving Hardy function and symmetric functions

Abstract

The Hardy matrix H n (x, α), the Hardy function per H n (x, α) and the generalized Vandermonde determinant det H n (x, α) are defined in this paper. By means of algebra and analysis theories together with proper hypotheses, we establish the following Minkowski-type inequality involving Hardy function:As applications, our inequality is used to estimate the lower bounds of the increment of a symmetric function. MSC: 26D15; 15A15

A Brunn-Minkowski-type inequality involving γ -mean variance and its applications

“…We remark here that inequality (2.2) had been extended in [18] and the authors obtained the following Minkowski-type inequality:…”