Problem 1750 (difficulty: 6/10)

Assume that \(\displaystyle f_n\in O(D)\) and \(\displaystyle f_n \to f\ (\ne const.)\) uniformly on \(\displaystyle D\). Show that if for all \(\displaystyle n\) there is a circline \(\displaystyle K_n\) whose image under \(\displaystyle f_n\) is a circline then \(\displaystyle f\) takes all circlines to circlines.

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