【摘要】 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.更多还原

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