Some inequalities for elementary mean values
Math. Comp. 42 (1984), 193-194
Primary 26D20; Secondary 26D15
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Abstract: Upper and lower bounds for the difference between the arithmetic and harmonic means of n positive numbers are obtained in terms of n and the largest and smallest of the numbers. Also, results of S. H. Tung , are used to obtain upper and lower bounds for the elementary mean values of Hardy, Littlewood, and Pólya.
H. Hardy, J.
E. Littlewood, and G.
Pólya, Inequalities, Cambridge, at the University
Press, 1952. 2d ed. MR 0046395
H. Tung, On lower and upper bounds of the
difference between the arithmetic and the geometric mean, Math. Comp. 29 (1975), 834–836. MR 0393393
(52 #14203), http://dx.doi.org/10.1090/S0025-5718-1975-0393393-9
- G. H. Hardy, J. E. Littlewood & G. Polya, Inequalities, Cambridge Univ. Press, Cambridge, 1952. MR 0046395 (13:727e)
- S. H. Tung, "On lower and upper bounds of the difference between the arithmetic and the geometric mean," Math. Comp., v. 29, 1975, pp. 834-836. MR 0393393 (52:14203)
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