Journal of Inequalities and Applications
Volume 2 (1998), Issue 4, Pages 387-395

A refinement of various mean inequalities

Takuya Hara,1 Mitsuru Uchiyama,1 and Sin-Ei Takahasi2

1Department of Mathematics, Fukuoka University of Education, Munakata, Fukuoka 811-4192, Japan
2Department of Basic Technology, Applied Mathematics and Physics, Yamagata University, Yonezawa 992-8510, Japan

Received 7 November 1997; Revised 9 January 1998

Copyright © 1998 Takuya Hara et al. 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.


A new refinement of the classical arithmetic mean and geometric mean inequality is given. Moreover, a new interpretation of the classical mean is given and this refinement theorem is generalized.