Some inequalities for elementary mean values

Meyer, Burnett

doi:10.1090/S0025-5718-1984-0725994-5

Mathematics of Computation

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Some inequalities for elementary mean values
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by Burnett Meyer PDF

Math. Comp. 42 (1984), 193-194 Request permission

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 ${M_p}$ of Hardy, Littlewood, and Pólya.

References

G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge, at the University Press, 1952. 2d ed. MR 0046395
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 393393, DOI 10.1090/S0025-5718-1975-0393393-9