Inequalities for the \(\lambda\)-weighted mixed arithmetic-geometric-harmonic means of sector matrices. (English) Zbl 1480.15023
For positive matrices, the comparison of weighted arithmetic, geometric and harmonic means is well known in the literature. In general, for sector matrices, arithmetic and harmonic means can be defined by the same formulas as positive matrices. However, the geometric mean is different because of the non-integer exponents of the matrices. M. Raïssouli et al. [C. R., Math., Acad. Sci. Paris 355, No. 6, 687–693 (2017; Zbl 1381.47011)]
defined the geometric mean for sector matrices in integral form. J.-L. Liu et al. [JP J. Algebra Number Theory Appl. 40, No. 4, 557–563 (2018; Zbl 1417.15025)]
proved the mixed arithmetic-geometric-mean inequality for two sector matrices. In this paper, the authors extend the above inequality for two sector matrices. Additionally, the authors give a generalization of their results for sums of \(n\) (\(n\ge 2\)) sector matrices.
Reviewer: Luyining Gan (Reno)
MSC:
| 15A45 | Miscellaneous inequalities involving matrices |
| 15A60 | Norms of matrices, numerical range, applications of functional analysis to matrix theory |
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