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. 2017;2017(1):209.
doi: 10.1186/s13660-017-1485-x. Epub 2017 Sep 7.

Extensions of interpolation between the arithmetic-geometric mean inequality for matrices

Mojtaba Bakherad  1 , Rahmatollah Lashkaripour  1 , Monire Hajmohamadi  1
Affiliations

Extensions of interpolation between the arithmetic-geometric mean inequality for matrices

Mojtaba Bakherad et al. J Inequal Appl. 2017.

Abstract

In this paper, we present some extensions of interpolation between the arithmetic-geometric means inequality. Among other inequalities, it is shown that if A, B, X are [Formula: see text] matrices, then [Formula: see text] where [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] are non-negative continuous functions such that [Formula: see text] and [Formula: see text] ([Formula: see text]). We also obtain the inequality [Formula: see text] in which m, n, s, t are real numbers such that [Formula: see text], [Formula: see text] is an arbitrary unitarily invariant norm and [Formula: see text].

Keywords: Cauchy-Schwarz inequality; Hilbert-Schmidt norm; arithmetic-geometric mean; unitarily invariant norm.

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