含剩余对称平均的不等式及其应用

定义 n个正实数 x1,x2 ,… ,xn的剩余对称平均 ∑k ( x) ,借助于数学归纳法及优超理论证明当 x∈Rn+ + 时有 :∑2 ( x)≥ ∑3( x)≥…≥ ∑n ( x)≥ A( x) .并将此结果用于正定矩阵 ,n维长方体及单形 .

Inequalities Involving Suplus Symmetric Means and Their Applications

We define the suplus symmetric mean ∑k(x) of n positive real numbers x 1, x 2, …, x n. By means of mathematical induction and the majorized theory, the inequalities ∑2(x)≥∑3(x)≥…≥∑n(x)≥A(x) (x∈Rn ++) are proved. As applications, these results are applied to positive definite matrice, n-dimensional cuboid and simplex.