论文标题
关于加权手段及其不平等现象
On weighted means and their inequalities
论文作者
论文摘要
在\ cite {psma}中，Pal等。引入了一些加权手段，并通过使用操作员单调函数的方法给出了一些相关的不平等。本文讨论了这些加权手段的构建，这立即导致那里确定的不平等现象。相关操作员版本也立即推导。根据我们的手段构造，我们通过使用诸如稳定且可稳定的手段等概念来研究三个加权算术/几何/谐波平均值的加权均值案例。最后，研究了功率对称手段，并给出了新的加权能力手段。
In \cite{PSMA}, Pal et al. introduced some weighted means and gave some related inequalities by using an approach for operator monotone functions. This paper discusses the construction of these weighted means in a simple and nice setting that immediately leads to the inequalities established there. The related operator version is here immediately deduced as well. According to our constructions of the means, we study all cases of the weighted means from three weighted arithmetic/geometric/harmonic means, by the use of the concept such as stable and stabilizable means. Finally, the power symmetric means are studied and new weighted power means are given.
