Liang Jin, Shi Guanghua
School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, 200240 China.
J Inequal Appl. 2017;2017(1):14. doi: 10.1186/s13660-016-1283-x. Epub 2017 Jan 10.
In this paper, we obtain two refinements of the ordering relations among Heinz means with different parameters via the Taylor series of some hyperbolic functions and by the way, we derive new generalizations of Heinz operator inequalities. Moreover, we establish a matrix version of Heinz inequality for the Hilbert-Schmidt norm. Finally, we introduce a weighted multivariate geometric mean and show that the weighted multivariate operator geometric mean possess several attractive properties and means inequalities.
在本文中，我们通过一些双曲函数的泰勒级数得到了具有不同参数的海因茨均值之间序关系的两种改进形式，并且顺便推导出了海因茨算子不等式的新推广。此外，我们建立了希尔伯特 - 施密特范数下的海因茨不等式的矩阵形式。最后，我们引入了加权多元几何均值，并表明加权多元算子几何均值具有几个吸引人的性质和均值不等式。
