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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: 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.


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

  • [1] R. E. Edwards, Functional analysis, theory and applications, Holt, New York, 1965. MR 36 #4308. MR 0221256 (36:4308)
  • [2] A. M. Fink and Max Jodeit, Jr., A generalization of the arithmetic-geometric means inequality, Proc. Amer. Math. Soc. 61 (1976), 255-261. MR 0427564 (55:595)
  • [3] D. S. Mitrinović, Analytic inequalities, Die Grundlehren der math. Wissenschaften, Band 165, Springer-Verlag, Berlin and New York, 1970. MR 43 #448. MR 0274686 (43:448)
  • [4] S. H. Tung, On lower and upper bounds of the difference between the arithmetic and the geometric mean, Math. Comput. 29 (1975), 834-836. MR 52 #14203. MR 0393393 (52:14203)
  • [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

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