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Continuously differentiable means


We consider continuously differentiable means, say-means. As for quasi-arithmetic means, we need an assumption that has no stationary points so that might be continuously differentiable. Introducing quasi-weights for-means would give a satisfactory explanation for the necessity of this assumption. As a typical example of a class of-means, we observe that a skew power mean is a composition of power means if is an integer.

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Correspondence to Jun Ichi Fujii.

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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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Fujii, J.I., Fujii, M., Miura, T. et al. Continuously differentiable means. J Inequal Appl 2006, 75941 (2006).

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