假設x及y是不同的正數，則 M = Mp (x , y) 稱冪平均數， L = L (x , y) 稱對數平均數。 Lin.[3]已證明 : 若Mp < L 則p 0 , 以及若L < Mq , 則q 。 我們將證明在某些限制下的x和y，當q < 時，L < Mq，並且證明當p > 0 ，L > Mp。 If x , y are distinct positive numbers, then M = Mp (x , y) is called the power mean of x and y . L = L (x , y) is called the Logarithmic mean of x and y . Lin.[3] has proved that : If Mp < L then p 0, and if L < Mq then q . We shall prove that L < Mq holds for some q such that q < , as well as L > Mp holds for some p such that p > 0 under certain restrictions on x and y .
