On lower and upper bounds of the difference between the arithmetic and the geometric mean
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- by S. H. Tung PDF
- Math. Comp. 29 (1975), 834-836 Request permission
Abstract:
Lower and upper bounds of the difference between the arithmetic and the geometric mean of n quantities are given here in terms of n, the smallest value a and the largest value A of given n quantities. Also, an upper bound for the difference, independent of n, is given in terms of a and A. All the bounds obtained are sharp.References
- Edwin F. Beckenbach and Richard Bellman, Inequalities, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Band 30, Springer-Verlag, Inc., New York, 1965. Second revised printing. MR 0192009
- Charles Loewner and Henry B. Mann, On the difference between the geometric and the arithmetic mean of $n$ quantities, Advances in Math. 5 (1970), 472–473 (1970). MR 279259, DOI 10.1016/0001-8708(70)90012-5
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Math. Comp. 29 (1975), 834-836
- MSC: Primary 26A87
- DOI: https://doi.org/10.1090/S0025-5718-1975-0393393-9
- MathSciNet review: 0393393