$\forall n\in \mathbb N$, Let $$f_n (x)=\underbrace{\cos(\cos(\cos(\cdots (\cos}_n(x\underbrace{))\cdots)}_n$$ It is known that $$\forall x\in\mathbb R,\space \lim_{n\rightarrow\infty}f_n(x)=0.7390851332\dots$$Does the convergence uniform?
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Tony Ma
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This question has been asked and answered several times in the past. See (1), (2), and (3) for examples. I'm personally rather fond of the version of the question to which I linked above, though I am biased in that regard. – Xander Henderson Feb 10 '18 at 12:40