Aequationes mathematicae

, Volume 77, Issue 1, pp 133–145

Invariance equation for generalized quasi-arithmetic means

Article

DOI: 10.1007/s00010-008-2939-5

Cite this article as:
Baják, S. & Páles, Z. Aequ. math. (2009) 77: 133. doi:10.1007/s00010-008-2939-5
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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).

26D1039B52

Keywords.

Invariance equationgeneralized quasi-arithmetic means

Copyright information

© Birkhäuser Verlag, Basel 2009

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of DebrecenDebrecenHungary