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  • Research Article
  • Open Access

Continuously differentiable means

  • 1Email author,
  • 2,
  • 3,
  • 4 and
  • 3
Journal of Inequalities and Applications20062006:75941

  • Received: 3 March 2006
  • Accepted: 12 September 2006
  • Published:


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.

Authors’ Affiliations

Information Science Division, Department of Arts and Sciences, Osaka Kyoiku University, Asahigaoka, Kashiwara, Osaka 582-8582, Japan
Department of Mathematics, Osaka Kyoiku University, Asahigaoka, Kashiwara, Osaka 582-8582, Japan
Group of Applied Mathematics and Physics, Department of Basic Technology, Yamagata University, Yonezawa 992-8510, Japan
Department of Mathematics, Shinshu University, Asahi, Matsumoto, Nagano 390-8621, Japan