Geodesic
Comparison of Arithmetic, Geometric, and Harmonic Means
Matematičeskie zametki, Tome 110 (2021) no. 1, pp. 110-118.

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: arithmetic mean, geometric mean, harmonic mean. 
@article{MZM_2021_110_1_a9,
     author = {L. V. Rozovskii},
     title = {Comparison of {Arithmetic,} {Geometric,} and {Harmonic} {Means}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {110--118},
     publisher = {mathdoc},
     volume = {110},
     number = {1},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_110_1_a9/}
}
TY  - JOUR
AU  - L. V. Rozovskii
TI  - Comparison of Arithmetic, Geometric, and Harmonic Means
JO  - Matematičeskie zametki
PY  - 2021
SP  - 110
EP  - 118
VL  - 110
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2021_110_1_a9/
LA  - ru
ID  - MZM_2021_110_1_a9
ER  - 
%0 Journal Article
%A L. V. Rozovskii
%T Comparison of Arithmetic, Geometric, and Harmonic Means
%J Matematičeskie zametki
%D 2021
%P 110-118
%V 110
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2021_110_1_a9/
%G ru
%F MZM_2021_110_1_a9
L. V. Rozovskii. Comparison of Arithmetic, Geometric, and Harmonic Means. Matematičeskie zametki, Tome 110 (2021) no. 1, pp. 110-118. http://geodesic.mathdoc.fr/item/MZM_2021_110_1_a9/

[1] D. I. Cartwright, M. J. Field, “A refinement of the arithmetic mean geometric mean inequality”, Proc. Amer. Math. Soc., 71 (1978), 36–38 | DOI | MR

[2] H. Alzer, “A new refinement of the arithmetic mean-geometric mean inequality”, Rocky Mountain J. Math., 27:3 (1997), 663–667 | DOI | MR

[3] 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 (2000), 163–173 | DOI | MR

[4] P. R. Mercer, “Refined arithmetic, geometric and harmonic mean inequalities”, Rocky Mountain J. Math., 33:4 (2003), 1459–1464 | DOI | MR

[5] S. G. From, R. Suthakaran, “Some new refinements of the arithmetic, geometric and harmonic mean inequalities with applications”, Appl. Math. Sci., 10:52 (2016), 2553–2569 | DOI

[6] D. S. Mitrinovic, J. E. Pecaric, A. M. Fink, Classical and New Inequalities in Analysis, Kluwer Acad. Publ., Dordrecht, 1995 | MR

[7] B. Rodin, “Variance and the inequality of arithmetic and geometric means”, Rocky Mountain J. Math., 47:2 (2017), 637–648 | DOI | MR

[8] L. Rozovsky, “Variance and the weighted AM–GM inequality”, Rocky Mountain J. Math., 2021 (to appear)

[9] I. Pinelis, “Exact upper and lower bounds of the difference between the arithmetic and geometric means”, Bull. Aust. Math. Soc., 92 (2015), 149–158 | DOI | MR