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Invariance equation for generalized quasi-arithmetic means

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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.

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Authors and Affiliations

  1. Institute of Mathematics, University of Debrecen, P.O. Box 12, H-4010, Debrecen, Hungary

    Szabolcs Baják & Zsolt Páles

Authors
  1. Szabolcs Baják
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  2. Zsolt Páles
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Corresponding author

Correspondence to Zsolt Páles.

Additional information

This research was supported by the Hungarian Research Fund (OTKA) Grant Nos. K-62316, NK-68040.

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Baják, S., Páles, Z. Invariance equation for generalized quasi-arithmetic means. Aequ. math. 77, 133–145 (2009). https://doi.org/10.1007/s00010-008-2939-5

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  • DOI: https://doi.org/10.1007/s00010-008-2939-5

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