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  • Research Article
  • Open Access

Convex sets and inequalities

  • 1Email author,
  • 2,
  • 3 and
  • 4
Journal of Inequalities and Applications20052005:964140

  • Received: 31 May 2002
  • Published:


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


© Takahasi et al. 2005