对称函数条件下的幂次和不等式探究

Exploring Power Sum Inequalities Under Symmetric Function Condition

本文主要探讨两组正实数列的对称函数条件相等下的幂次和不等式问题,即(x_(1),x_(2),…,x_(n),)和(y_(1),y_(2),…y_(n)),用e_(k)(x)e_(k)(y)分别表示x_(1),x_(2),…,x_(n)和y_(1),y_(2),…,y_(n)的第k个初等对称多项式,得出了若e_(k)≥e_(k)(y),e_(i)(x)=e_(i)(y)(1≤h≤n,i≠h),则∑_(k=1)n_(x_(k)^(p))与∑_(k=1)^(n)_(y_(k))^(p)的大小关系.