Annals of Functional Analysis
- Ann. Funct. Anal.
- Volume 7, Number 2 (2016), 348-357.
Some matrix inequalities for weighted power mean
In this paper, we prove that, for any positive definite matrices , and real numbers with and , we have
where and stand for weighted arithmetic and power mean, respectively. In the special cases when , this inequality can be considered as a generalization of harmonic-arithmetic and geometric-arithmetic means inequalities and their reverses.
Applying this inequality, some inequalities for the Heinz mean and determinant inequalities related to weighted power means are obtained.
Ann. Funct. Anal., Volume 7, Number 2 (2016), 348-357.
Received: 29 June 2015
Accepted: 18 October 2015
First available in Project Euclid: 8 April 2016
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Khosravi, Maryam. Some matrix inequalities for weighted power mean. Ann. Funct. Anal. 7 (2016), no. 2, 348--357. doi:10.1215/20088752-3544480. https://projecteuclid.org/euclid.afa/1460141560