An inconsistency equation involving means

Volume 115 / 2009

Roman Ger, Tomasz Kochanek Colloquium Mathematicum 115 (2009), 87-99 MSC: Primary 39B22; Secondary 26A24. DOI: 10.4064/cm115-1-8

Abstract

We show that any quasi-arithmetic mean $A_{\varphi}$ and any non-quasi-arithmetic mean $M$ (reasonably regular) are inconsistent in the sense that the only solutions $f$ of both equations $$ f(M(x,y)) = A_{\varphi}(f(x), f(y)) $$ and $$ f(A_{\varphi}(x,y)) = M(f(x), f(y)) $$ are the constant ones.

Authors

  • Roman GerInstitute of Mathematics
    Silesian University
    Bankowa 14
    40-007 Katowice, Poland
    e-mail
  • Tomasz KochanekInstitute of Mathematics
    Silesian University
    Bankowa 14
    40-007 Katowice, Poland
    e-mail

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