International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1982 / Article

Open Access

Volume 5 |Article ID 718951 | https://doi.org/10.1155/S0161171282000313

Christopher Olutunde Imoru, "The power mean and the logarithmic mean", International Journal of Mathematics and Mathematical Sciences, vol. 5, Article ID 718951, 7 pages, 1982. https://doi.org/10.1155/S0161171282000313

The power mean and the logarithmic mean

Received03 Jul 1979
Revised24 Mar 1980

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-InyThe 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.

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.


More related articles

 PDF Download Citation Citation
 Order printed copiesOrder
Views107
Downloads589
Citations

We are committed to sharing findings related to COVID-19 as quickly as possible. We will be providing unlimited waivers of publication charges for accepted research articles as well as case reports and case series related to COVID-19. Review articles are excluded from this waiver policy. Sign up here as a reviewer to help fast-track new submissions.