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注： 有关琴生不等式 (jensen's inequality)在高中的应用，小π已经在前面推文中介绍，链接： 748期【导数】琴生不等式在高中的应用 感兴趣的同学可以移步到以上链接。 最后， 根据 jensen 不等式： [引理 3] 对于任意的正定矩阵 r>0 ，以及所有连续可微的向量函数 \omega: 考虑jensen不等式 \left (\sum_ {i=1}^k\frac {a_i} {\sum_ {j=1}^k a_j} x_i\right)^n\le\sum_ {i=1}^k \frac {a_i} {\sum_ {j=1}^k a_j} x_i^n\\ i.e.

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加权jensen不等式：设 \lambda _ {i}\in r^ {+} 且 \sum_ {i=1}^ {n} {\lambda_i}=1 , f (x) 是区间 (a,b) 内的严格下凸函数，则对于 (a,b) 内 \forall x_ {1},x_ {2},.,x_ {n} ,有

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