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Results tagged with fixed-point-theorems
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user 243942
Fixed-point theorem is a result about existence of fixed points, i.e. points fulfilling $F(x)=x$, under some conditions on the function $F$. Results of this type appear in many areas of mathematics, e.g. functional analysis (Banach), algebraic topology (Brouwer), lattice theory (Knaster-Tarski, Kleene) etc.
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How to show that $1$ is an attracting period-2 point.
I am trying to solve this question, here is my solution, is it correct?
Question: Let $f(x)=-\frac{1}{2}x^2-x+\frac{1}{2}$. Show that $1$ is an attracting period-2 point.
Solution:
$$f(1)=-1$$$$f( …
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