Journal of Inequalities and Applications
Volume 2005 (2005), Issue 2, Pages 107-117

Convex sets and inequalities

Sin-Ei Takahasi,1 Yasuji Takahashi,2 Shizuo Miyajima,3 and Hiroyuki Takagi4

1Department of Basic Technology, Yamagata University, Yonezawa 992-8510, Japan
2Department of Systems Engineering, Okayama Prefectural University, Soja, Okayama 719-1197, Japan
3Department of Mathematics, Tokyo University of Science, Shinjuku-ku, Wakamiya 26, Tokyo 162-8601, Japan
4Department of Mathematical Sciences, Faculty of Science, Shinshu University, Matsumoto 390-8621, Japan

Received 31 May 2002; Revised 26 December 2004

Copyright © 2005 Sin-Ei Takahasi 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.


We consider a natural correspondence between a family of inequalities and a closed convex set. As an application, we give new types of power mean inequalities and the Hölder-type inequalities.