On lower and upper bounds of the difference between the arithmetic and the geometric mean
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.
- Edwin F. Beckenbach and Richard Bellman, Inequalities, Ergebnisse der Mathematik und ihrer Grenzgebiete, N.F., Bd. 30, Springer-Verlag, New York, Inc., 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 https://doi.org/10.1016/0001-8708%2870%2990012-5
E. F. BECKENBACH & R. E. BELLMAN, Inequalities, 2nd rev. ed., Ergebnisse der Mathematik und ihrer Grenzgebiete, N. F., Band 30, Springer-Verlag, New York, 1965. MR 33 #236.
C. LOEWNER & H. B. MANN, "On the difference between the geometric and the arithmetic mean of n quantities," Advances in Math., v. 5, 1971, pp. 472-473. MR 43 #4982.
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