1 Correction to: Aequat. Math. 94 (2020), 679–687 https://doi.org/10.1007/s00010-019-00674-5

We made a simple but near-fatal mistake in the statement of Theorem 6. Namely instead of the assumption ”\(F\left( \cdot ,t\right) \) is continuous for each \(t \in (0,+\infty )\)” there should be written ”\(F\left( (x,y),\cdot \right) \) is continuous for each \((x,y) \in I^2\)”. Consequently, the proper formulation of the theorem is as follows:

Theorem 6

Let \(F: I^2\times (0,+\infty )\rightarrow I^2\) be a function such that \(F\left( (x,y),\cdot \right) \) is continuous for each \((x,y) \in I^2\). The function F is a continuous semiflow of pairs of weighted quasi-arithmetic means if and only if there exist a function \(f\in \mathcal {CM}(I)\) and numbers \(p, q \in (0,1)\) such that \(p\ge q\) and

$$\begin{aligned} F\left( \cdot ,t\right) =\left( A^f_{\mu (t)},A^f_{\nu (t)}\right) , \qquad t \in (0,+\infty ), \end{aligned}$$

where the functions \( \mu , \nu :(0,+\infty )\rightarrow (0,1)\) are given by (9).