A refinement of the arithmetic mean-geometric mean inequality
Authors:
D. I. Cartwright and M. J. Field
Journal:
Proc. Amer. Math. Soc. 71 (1978), 36-38
MSC:
Primary 26A87
DOI:
https://doi.org/10.1090/S0002-9939-1978-0476971-2
MathSciNet review:
0476971
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Abstract | References | Similar Articles | Additional Information
Abstract: Upper and lower bounds are given for the difference between the arithmetic and geometric means of n positive real numbers in terms of the variance of these numbers.
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- [3] D. S. Mitrinović, Analytic inequalities, Springer-Verlag, New York-Berlin, 1970. In cooperation with P. M. Vasić. Die Grundlehren der mathematischen Wissenschaften, Band 165. MR 0274686
- [4] 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, https://doi.org/10.1090/S0025-5718-1975-0393393-9
- [5] K. S. Williams, Problem 247, Eureka 3 (1977), 131.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1978-0476971-2
Keywords:
Arithmetic mean-geometric mean inequality
Article copyright:
© Copyright 1978
American Mathematical Society