- E101
[0TH]Prerequisites:[0VP].Let \((X,d)\) be a compact metric space, and let \(f:X→ X\) be such that
\[ ∀ x,y∈ X, x≠ y⇒ d(f(x),f(y)) {\lt} d(x,y)\quad . \]Show that \(f\) has a single fixed point \(\overline x\).
Let \(x_ 0\in X\) and define \(x_{n+1}=f(x_ n)\) by recurrence: show that \(\lim _ n x_ n = \overline x\).
This result is sometimes called Edelstein’s Theorem.
Solution 1
EDB — 0TH
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English
Authors:
"Mennucci , Andrea C. G."
.
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