Asymptotic dynamics of generalized Kantorovich operators

We characterize the family of continuous functions $f\in C([0,1])$ such that the iterates ${\widehat{T}}_i^{k}f$ converge uniformly on $[0,1]$, where ${\widehat{T}}_i$ is a generalized Kantorovich operator. This gives an affirmative answer to the problem raised in 2021 by Acu and Rasa.