Journal of Inequalities and Applications 
Volume 2005 (2005), Issue 2, Pages 107-117
doi:10.1155/JIA.2005.107

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

Abstract

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.