Silvestru Sever Dragomir Mathematics, College of Engineering & Science, Victoria University, PO Box 14428, Melbourne City, MC 8001, Australia
DST-NRF Centre of Excellence in the Mathematical and Statistical Sciences, School of Computer Science, & Applied Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg 2050, South Africa

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Assume that Aj, j ∈ {1, … , m} are positive definite matrices of order n. In this paper we prove among others that, if 0 < l InAj, j ∈ {1, … , m} in the operator order, for some positive constant l, and In is the unity matrix of order n, then


where Pk ≥ 0 for k ϵ {1, …, m} and j=1mPj=1.

  • [1]

    BECKENBACH, E. F. AND BELLMAN, R. Inequalities. Berlin-Heidelberg-New York, 1971.

  • [2]

    CARTWRIGHT, D. I. AND FIELD, M. J. A refinement of the arithmetic mean-geometric mean inequality. Proc. Amer. Math. Soc. 71 (1978), 3638.

    • Search Google Scholar
    • Export Citation
  • [3]

    LI, Y., YONGTAO, L., HUANG FENG Z., AND LIU, W. Inequalities regarding partial trace and partial determinant. Math. Inequal. Appl. 23 (2) (2020), 477485.

    • Search Google Scholar
    • Export Citation
  • [4]

    LIN, M. AND SINNAMON, G. Revisiting a sharpened version of Hadamard’s determinant inequality. Linear Algebra Appl. 606 (2020), 192200.

    • Search Google Scholar
    • Export Citation
  • [5]

    LIU, J.-T., WANG Q.-W., AND SUN, F.-F. Determinant inequalities for Hadamard product of positive definite matrices. Math. Inequal. Appl. 20 (2) (2017), 537542.

    • Search Google Scholar
    • Export Citation
  • [6]

    LUO, W. Further extensions of Hartfiel’s determinant inequality to multiple matrices. Spec. Matrices 9 (2021), 7882.

  • [7]

    ITO, M. Estimations of the weighted power mean by the Heron mean and related inequalities for determinants and traces. Math. Inequal. Appl. 22 (3) (2019), 949966.

    • Search Google Scholar
    • Export Citation
  • [8]

    MIRSKY, L. An inequality for positive definite matricies. Amer. Math. Monthly 62 (1955), 428430.

  • [9]

    MITRINOVIS, D. S., PESARIS, J. E., AND FINK, A. M. Classical and New Inequalities in Analysis. Kluwer Acedemic Publishers, 1993.

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Editor in Chief: László TÓTH (University of Pécs)

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