International Journal of Mathematics and Mathematical Sciences
Volume 5 (1982), Issue 2, Pages 337-343
doi:10.1155/S0161171282000313

The power mean and the logarithmic mean

Abstract

In a very interesting and recent note, Tung-Po Lin [1] obtained the least value q and the greatest value p such that Mp<L<Mqis valid for all distinct positive numbers x and y where Ms=(xs+ys2)1s   and   L=x−yIn x-In yThe object of this paper is to give a simpler proof than Lin's of a more general result. More precisely, the author obtained the classes of functions fα and hα, α∈R such that In fα(t)−hα(t)[t1/α+1]−α>0,   t>1.