Sharp bounds for the difference between the arithmetic and geometric means

J. M. Aldaz

Published 2012-03-20Version 1

We present sharp bounds for $\sum_{i=1}^n \alpha_i x_i - \prod_{i=1}^n x_i^{\alpha_i}$ in terms of the variance of the vector $(x_1^{1/2},...,x_n^{1/2})$.