摘要
指出文献［１］的一个证明错误，同时给出了另一个性质较好的下界：设ｘ，ｙ是两个相异正数，Ｐ是任意正实数，则（ｘｙ）１Ｐ＋１ｘ－ｙＰ（ｘ１／Ｐ－ｙ１／Ｐ）ＰＰ＋１＜ｘ－ｙｌｎｘ－ｌｎｙ．
We point out a mistake in literature and give another lower bound with better properties as follows : suppose that x and y are two different positive numbers, and P is a positive real number , then (xy) 1P+1 x-yP(x 1/P -y 1/P )] PP+1 <x-y ln x- ln y.
关键词
对数平均
r次幂积分平均
下界
logarithm mean
mean of integration of powe r
lower bound.
