Young-type inequalities and their matrix analogues
Young-type inequalities and their matrix analogues
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杨氏型不等式及其矩阵类似物
DOI：
10.1080/03081087.2014.891588
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发表时间：
2015
影响因子：
1.1
通讯作者：
A. Kovacec
中科院分区：
文献类型：
--
作者：
H. Alzer;C. D. da Fonseca;A. Kovacec
给出了几个新的正真实的数的Young型不等式，并应用所得结果得到了矩阵的类似结果.其中，对于真实的数，和，与，我们证明了不等式，其中和，分别是（加权）算术和几何平均值的正真实的数和与。此外，我们证明了这两个边界是尖锐的。正定矩阵的双重不等式是这种情况下的矩阵类似的一个例子。我们的结果推广了Kittaneh，Manasrah，Hirzallah和Feng建立的一些新的不等式. Furuichi和Minculete给出的商及其矩阵类似物的估计也得到了改进。
We present several new Young-type inequalities for positive real numbers and we apply our results to obtain the matrix analogues. Among others, for real numbers , and , with and , we prove the inequalitieswhere and are, respectively, the (weighted) arithmetic and geometric means of the positive real numbers and with . In addition, we show that both bounds are sharp. An example of a matrix analogue for the case is the double-inequalityfor positive definite matrices . Our results extend some fresh inequalities established by Kittaneh, Manasrah, Hirzallah and Feng. Estimates for the quotient and its matrix analogues given by Furuichi and Minculete are also improved.