, Volume 77, Issue 1-2, pp 133-145

Invariance equation for generalized quasi-arithmetic means

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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.