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Some inequalities for elementary mean values
Author:
Burnett Meyer
Journal:
Math. Comp. 42 (1984), 193-194
MSC:
Primary 26D20; Secondary 26D15
MathSciNet review:
725994
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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 [2], are used to obtain upper and lower bounds for the elementary mean values  of Hardy, Littlewood, and Pólya.
- [1]
G.
H. Hardy, J.
E. Littlewood, and G.
Pólya, Inequalities, Cambridge, at the University
Press, 1952. 2d ed. MR 0046395
(13,727e)
- [2]
S.
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
- [1]
- G. H. Hardy, J. E. Littlewood & G. Polya, Inequalities, Cambridge Univ. Press, Cambridge, 1952. MR 0046395 (13:727e)
- [2]
- 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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Additional Information
DOI:
http://dx.doi.org/10.1090/S0025-5718-1984-0725994-5
PII:
S 0025-5718(1984)0725994-5
Article copyright:
© Copyright 1984 American Mathematical Society
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