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

Xinh Thi Dinh (), Huy Quoc Duong () and Hue Ngoc Nguyen ()
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Xinh Thi Dinh: Tay Nguyen University
Huy Quoc Duong: Tay Nguyen University
Hue Ngoc Nguyen: Tay Nguyen University

Indian Journal of Pure and Applied Mathematics, 2022, vol. 53, issue 4, 1122-1127

Abstract: 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.

Keywords: Arithmetic–geometric mean inequality; Young inequality; Positive definite matrix; Weak sub-majorization; 15A45; 26D15; 15B48 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13226-022-00223-y

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