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

The power mean and the logarithmic mean

Department of Mathematics, University of Ife, Ile-Ife, Oyo State, Nigeria

Received 3 July 1979; Revised 24 March 1980

Copyright © 1982 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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)1sandL=xyInx-Iny

The 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, αR such that Infα(t)hα(t)[t1/α+1]α>0,t>1.