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Continuously differentiable means

Abstract

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 (https://creativecommons.org/licenses/by/2.0), 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). https://doi.org/10.1155/JIA/2006/75941

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