二重幂平均不等式的优化与机器实现

Optimization and Computer Actualization of Inequalities Involving the Double Power Means

定义了正实数组a的t次二重幂平均M[t]m,n(a;α;λ),获得了使不等式M[r]m,n(a;α;λ)≤(≥)Mn[θ](a)成立的机器可实现的充要条件和充分条件,借助于Mathematica数学软件给出了一些算例.这里,Mn[θ](a)为正实数组a的θ次幂平均,m,n≥2,min{α}<θ<max{α},实数r>0,采用的方法是降维法.

For a set of positive quantities, the double power mean Mm,n^[r]（ a, a ; λ. ） of order t is definited. .We obtain a sufficient and necessary condition such that Mm,n^[r] （a;a;λ） ≤（≥） Mn^[θ] （a） holds, and can be dealed with computer. Using Mathematica we give several numerical examples. Here Mn^[θ]（a） is the power mean of the set a and order θ, and m, n ≥ 2, min { a } 〈 θ 〈 max{ a }, r 〉 0. Methods used here are procedures of descending dimension.