Open Access

Convex sets and inequalities

  • Sin-Ei Takahasi1Email author,
  • Yasuji Takahashi2,
  • Shizuo Miyajima3 and
  • Hiroyuki Takagi4
Journal of Inequalities and Applications20052005:964140

Received: 31 May 2002

Published: 1 June 2005


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.

Authors’ Affiliations

Department of Basic Technology, Yamagata University
Department of Systems Engineering, Okayama Prefectural University
Department of Mathematics, Tokyo University of Science
Department of Mathematical Sciences, Faculty of Science, Shinshu University


© Takahasi et al. 2005