Timeline for When is a fixed point of f^n a fixed point of f?
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Jan 10, 2013 at 14:31 | comment | added | Pietro Majer | (or, also: if $f^n$ is a contraction on a complete metric space, it has a unique fixed point $x$; but $f(x)$ is a fixed point of $f^n$ too, so by the uniqueness $x=f(x)$.) | |
| Sep 18, 2012 at 19:48 | comment | added | jbc | It is a trivial remark (not due to me) that if a mapping $ f $ on a set $ X $ (no metric required) has a unique fixed point, then this is also a fixed point for any mapping which commutes with $f$. This implies immediately that a mapping on a complete metric space has a fixed point whenever some iterate is a contraction. No continuity assumption is required. | |
| Jul 19, 2010 at 15:40 | vote | accept | user3014 | ||
| Jul 18, 2010 at 22:37 | history | answered | Pietro Majer | CC BY-SA 2.5 |