摘要
本文把文[1—3]的结果推广为:设 x 和 y 是正数,p 是实数,则(x-y)/(1nx-1ny)≥(xy)^(p/2)((x^p+y^p)/2)^((1-p)/p):等号仅当 x=y 时取.
In this paper,the results of[1],[2]and[3]are generalized as follows: Theorm Let x and y be positive numbers,and let p be a real number. Then (x-y)/(1nx-1ny)≥(xy)^(p/2)((x^p+y^p)/2)^((1-p)/p), with equality only if x=y.
关键词
对数平均
P
次幂平均
下界
Logarithmic mean
mean of order p
lower bound
