New sharp bounds for identric mean in terms of logarithmic mean and arithmetic mean

摘要

Let x,y > 0 with x = y . We give new sharp bounds for identric mean I = e .1 (x x /y y ) 1/(x.y) in terms of logarithmic mean L =(x . y) / (ln x . ln y) and arithmetic mean A =(x + y) /2: 1 2 L p 0 + 1 2 A p 0 1/p 0 < I < 1 2 L . p 0 + 1 2 A . p 0 1/ . p 0 , where p 0 = 8/5and . p 0 =(ln 2)/(1 . ln 2) are the best possible constants.