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

References [Enhancements On Off] (What's this?)

  • [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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Article copyright: © Copyright 1984 American Mathematical Society

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