Aequationes mathematicae

, Volume 77, Issue 1–2, pp 133–145

Invariance equation for generalized quasi-arithmetic means

Article

Summary.

In this paper, the invariance equation
$$(\varphi_{1} + \varphi_{2})^{-1} (\varphi_{1}(x) + \varphi_{2}(y)) + (\psi_{1} + \psi_{2})^{-1}(\psi_{1}(x) + \psi_{2}(y)) = x + y$$
is solved under four times continuous differentiability of the unknown functions φ1, φ2, ψ1, ψ2.

Mathematics Subject Classification (2000).

26D10 39B52 

Keywords.

Invariance equation generalized quasi-arithmetic means 

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Copyright information

© Birkhäuser Verlag, Basel 2009

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of DebrecenDebrecenHungary

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