Minkowski-type inequalities involving Hardy function and symmetric functions

AbstractThe Hardy matrix Hn(x,α), the Hardy function perHn(x,α) and the generalized Vandermonde determinant detHn(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: [perHn(x+y,α)]1|α|⩾[perHn(x,α)]1|α|+[perHn(y,α)]1|α|. As applications, our inequality is used to estimate the lower bounds of the increment of a symmetric function.MSC:26D15, 15A15.