%0 Journal Article %T Convex sets and inequalities %A Takahasi Sin-Ei %A Takahashi Yasuji %A Miyajima Shizuo %A Takagi Hiroyuki %J Journal of Inequalities and Applications %D 2005 %I Springer %X 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 H lder-type inequalities. %U http://www.journalofinequalitiesandapplications.com/content/2005/964140