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Convex sets and inequalities


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.

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Correspondence to Sin-Ei Takahasi.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Takahasi, SE., Takahashi, Y., Miyajima, S. et al. Convex sets and inequalities. J Inequal Appl 2005, 964140 (2005).

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