Geodesic
Comparison of Discrete Mixed Means Containing Symmetric Functions
Matematičeskie zametki, Tome 80 (2006) no. 2, pp. 262-269 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove inequalities for mixed generalized means; from these inequalities we obtain analogs or generalizations of inequalities due to Ness, to Carlson, Meany, and Nelson, to Godunova, and to Marcus and Minc, etc.
Keywords: discrete mixed mean, strictly monotone continuous function, generalized mean, concave and convex function, symmetric function, Jessen's inequality, Jensen's inequality. 
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     title = {Comparison of {Discrete} {Mixed} {Means} {Containing} {Symmetric} {Functions}},
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R. Kh. Sadikova. Comparison of Discrete Mixed Means Containing Symmetric Functions. Matematičeskie zametki, Tome 80 (2006) no. 2, pp. 262-269. http://geodesic.mathdoc.fr/item/MZM_2006_80_2_a11/

[1] W. Ness, “Das arithemetische und das geometrische Mittel”, Prax. Math., 8:11 (1964), 293–296

[2] B. Carlson, R. Meany, S. Nelson, “Mixed arithmetic and geometric means”, Pacif. J. Math., 38:2 (1971), 343–349 | MR | Zbl

[3] E. K. Godunova, Neravenstva s vypuklymi funktsiyami, Diss. ... kand. fiz.-matem. nauk, MGPI, M., 1965

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[6] O. Shisha, G. Cargo, “On comparable means”, Pacif. J. Math., 4:3 (1964), 1053–1059 | MR