Problem:
Let $C\subset X$ closed subset of the Banach space $X$. Suppose that for the function $K:C \to C$, its nth iteration $K^{n}:C\to C$ is a contraction. Show that $K$ has a unique fixed point.
For me this is exactly Weissinger's fixed point theorem, but apparently its not cause this was on a test and I got 0 on this one.
Thanks so much for the help, <3.