Journal of Inequalities and Applications
Volume 2005 (2005), Issue 1, Pages 15-23

A reconsideration of Hua's inequality

Hiroyuki Takagi,1 Takeshi Miura,2 Tadashi Kanzo,3 and Sin-Ei Takahasi2

1Department of Mathematical Sciences, Faculty of Science, Shinshu University, Matsumoto 390-8621, Japan
2Department of Basic Technology, Applied Mathematics and Physics, Yamagata University, Yonezawa 992-8510, Japan
3College of Engineering, Kanto Gakuin University, Yokohama 236-8501, Japan

Received 11 July 2004

Copyright © 2005 Hiroyuki Takagi 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.


The inequality discovered by L. K. Hua in 1965 has been generalized in several directions. In this paper, we adopt a certain conjugate method to give a simple and fundamental inequality on two functions on a semigroup, which is the key to the proof of many generalizations of Hua's inequality.