Open Access

A reconsideration of Hua's inequality

  • Hiroyuki Takagi1Email author,
  • Takeshi Miura2,
  • Tadashi Kanzo3 and
  • Sin-Ei Takahasi2
Journal of Inequalities and Applications20052005:150678

Received: 11 July 2004

Published: 1 February 2005


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.

Authors’ Affiliations

Department of Mathematical Sciences, Faculty of Science, Shinshu University, Matsumoto, Japan
Department of Basic Technology, Applied Mathematics and Physics, Yamagata University, Yonezawa, Japan
College of Engineering, Kanto Gakuin University, Yokohama, Japan


© Takagi et al. 2005