Comparison of differences between arithmetic and geometric means

Authors

  • J. M. Aldaz Departamento deMatemáticas, Universidad Autónoma deMadrid, Cantoblanco 28049, Madrid, Spain.

DOI:

https://doi.org/10.5556/j.tkjm.42.2011.747

Keywords:

Self-improvement, Arithmetic-Geometric inequality

Abstract

We complement a recent result of S. Furuichi, by showing that the differences $\sum_{i=1}^n \alpha_i x_i - \prod_{i=1}^n x_i^{\alpha_i}$ associated to distinct sequences of weights are comparable, with constants that depend on the smallest and largest quotients of the weights.

Author Biography

J. M. Aldaz, Departamento deMatemáticas, Universidad Autónoma deMadrid, Cantoblanco 28049, Madrid, Spain.

Professor at the Math. Department.

References

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Shigeru Furuichi, A refinement of the arithmetic-geometric mean inequality, arXiv:0912.5227.

Ronald E. Glaser, The ratio of the geometric mean to the arithmetic mean for a random sample from a gamma distribution, J. Amer. Statist. Assoc.,71(1976), 480--487.

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Published

2011-12-31

How to Cite

Aldaz, J. M. (2011). Comparison of differences between arithmetic and geometric means. Tamkang Journal of Mathematics, 42(4), 453–462. https://doi.org/10.5556/j.tkjm.42.2011.747

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Section

Papers