Journal of Inequalities and Applications 
Volume 2005 (2005), Issue 1, Pages 15-23
doi:10.1155/JIA.2005.15

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

Abstract

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.