Sharp bounds for the difference between the arithmetic and geometric means

Details Sharp bounds for the difference between the arithmetic and geometric means Sharp bounds for the difference between the arithmetic and geometric means

2012-03-20

arxiv.org/abs/1203.4454v1

Mathematics

Classical Analysis and ODEs

7 pages

Scientific paper

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
$(x_1^{1/2},...,x_n^{1/2})$.

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