Nonconvex functions and separation by power means

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In this note we show that, for a nonconvex function defined on a real interval, there exists a point where this function behaves like a strictly concave function. Due to this result, global convexity can be characterized as pointwise convexity everywhere. As an application, a necessary and sufficient condition for the separability of quasiarithmetic means with power means is obtained.

Original languageEnglish
Pages (from-to)169-176
Number of pages8
JournalMathematical Inequalities and Applications
Issue number2
Publication statusPublished - Apr 2000



  • Convexity
  • Power means
  • Quasiarithmetic means
  • Separation

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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