Abstract
The main purpose of the paper is to strengthen the results of P. R. Mercer (2003) concerning the comparison of arithmetic, geometric, and harmonic weighted means.
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References
D. I. Cartwright and M. J. Field, “A refinement of the arithmetic mean-geometric mean inequality,” Proc. Amer. Math. Soc. 71, 36–38 (1978).
H. Alzer, “A new refinement of the arithmetic mean-geometric mean inequality,” Rocky Mountain J. Math. 27 (3), 663–667 (1997).
A. M. Mercer, “Bounds for \(A\)–\(G\), \(A\)–\(H\), \(G\)–\(H\) and a family of inequalities of Ky Fan’s type, using a general method,” J. Math. Anal. Appl. 243, 163–173 (2000).
P. R. Mercer, “Refined arithmetic, geometric and harmonic mean inequalities,” Rocky Mountain J. Math. 33 (4), 1459–1464 (2003).
S. G. From and R. Suthakaran, “Some new refinements of the arithmetic, geometric and harmonic mean inequalities with applications,” Appl. Math. Sci. 10 (52), 2553–2569 (2016).
D. S. Mitrinovic, J. E. Pecaric, and A. M. Fink, Classical and New Inequalities in Analysis (Kluwer Acad. Publ., Dordrecht, 1995).
B. Rodin, “Variance and the inequality of arithmetic and geometric means,” Rocky Mountain J. Math. 47 (2), 637–648 (2017).
L. Rozovsky, “Variance and the weighted AM–GM inequality,” Rocky Mountain J. Math. (2021) (in press).
I. Pinelis, “Exact upper and lower bounds of the difference between the arithmetic and geometric means,” Bull. Aust. Math. Soc. 92, 149–158 (2015).
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Translated from Matematicheskie Zametki, 2021, Vol. 110, pp. 110-118 https://doi.org/10.4213/mzm13045.
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Rozovsky, L.V. Comparison of Arithmetic, Geometric, and Harmonic Means. Math Notes 110, 118–125 (2021). https://doi.org/10.1134/S0001434621070129
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DOI: https://doi.org/10.1134/S0001434621070129