Minkowski-type inequalities involving Hardy function and symmetric functions

作者：Wen, JiaJin; Wu, ShanHe; Han, TianYong

来源：JOURNAL OF INEQUALITIES AND APPLICATIONS, 2014, 2014(1): 186.

DOI：10.1186/1029-242X-2014-186

• Hardy matrix
• Hardy function
• Minkowski's inequality
• homogeneous and symmetric polynomial
• symmetric function

The Hardy matrix H-n(x, alpha), the Hardy function per H-n( x, alpha) and the generalized Vandermonde determinant det H-n( x, alpha) 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:
[per H-n( x + y, alpha)](1/vertical bar alpha vertical bar) >= [per H-n( x, alpha)](1/vertical bar alpha vertical bar) + [per H-n(y, alpha)](1/vertical bar alpha vertical bar)
As applications, our inequality is used to estimate the lower bounds of the increment of a symmetric function.

• 出版日期2014-5-13
• 单位龙岩学院; 成都大学