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Two new extensions of the weighted arithmetic–geometric mean inequality via weak sub-majorization

Author

Listed:
  • Xinh Thi Dinh

    (Tay Nguyen University)

  • Huy Quoc Duong

    (Tay Nguyen University)

  • Hue Ngoc Nguyen

    (Tay Nguyen University)

Abstract

In this paper we give some new power-type refinements and reverses of the weighted arithmetic–geometric mean inequality. Our result is a remarkable generalization of the one due to Furuichi (J Math Inequal 5(1):21–31, 2011), Manasrah and Kittaneh (J Math Anal Appl 361(1):262–269, 2010, Linear Multilinear Algebra 59(9):1031–1037, 2011). When the power is a positive integer number, our result is also a refinement of a very recent generalization established by Ighachane et al. (Math Inequal Appl 23(3):1079–1085, 2020) for this inequality. As an application, we provide some generalized inequalities for determinants of positive definite matrices.

Suggested Citation

  • Xinh Thi Dinh & Huy Quoc Duong & Hue Ngoc Nguyen, 2022. "Two new extensions of the weighted arithmetic–geometric mean inequality via weak sub-majorization," Indian Journal of Pure and Applied Mathematics, Springer, vol. 53(4), pages 1122-1127, December.
    • Handle: RePEc:spr:indpam:v:53:y:2022:i:4:d:10.1007_s13226-022-00223-y
    DOI: 10.1007/s13226-022-00223-y
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