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樊畿不等式 - Wikipedia

樊畿不等式

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樊畿(Ky Fan)不等式，是华裔数学家樊畿发现的一个不等式，它是說：

如果x_1, \ldots, x_n是正數，所有xi都符合0 < x_i \le {1 \over 2}，那麼

\frac{\left(\prod_{i=1}^n x_i\right)^{1/n}}{\left(\prod_{i=1}^n (1-x_i)\right)^{1/n}} \le \frac {{1 \over n} \sum_{i=1}^n x_i}{{1 \over n} \sum_{i=1}^n (1-x_i)}，

等式成立當且僅當x_1 = \cdots = x_n。

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