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Results tagged with fixed-point-theorems
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user 3014
A fixed-point theorem is a result saying that a function $F$ will have at least one fixed point (a point $x$ for which $F(x) = x$), under some conditions on $F$ that can be stated in general terms.
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When is a fixed point of f^n a fixed point of f?
Let $E$ be a Banach space and $f:E\to E$ be a continuous map. By $f^n$ we denote the $n$-th iterate of $f$, i.e. $f^n:=\underbrace{f\circ f\circ\cdots \circ f}_{\text{n times}}$. Let $x_0$ denote a fi …
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