Comparison of differences between arithmetic and geometric means

J. M. Aldaz

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.

Keywords


Self-improvement, Arithmetic-Geometric inequality

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References


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DOI: http://dx.doi.org/10.5556/j.tkjm.42.2011.747

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