Comparison of differences between arithmetic and geometric means

J. M. Aldaz

Published 2010-01-27, updated 2010-10-07Version 2

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.