Journal of Inequalities and Applications 
Volume 2 (1998), Issue 4, Pages 387-395
doi:10.1155/S1025583498000253

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

Abstract

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.