# Fixed point syntax!

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• December 20th 2010, 02:56 AM
cantona
Fixed point syntax!
Hi everyone!

I am a little bit confused how write this:

My map is: $F(f)(x)=\frac{1}{2}f(x)-\frac{3}{5}$. I must calculated a fixed point. I know how to do that and I now how much it is. But problem is in syntax. Is that the right one: $F(f(x_0))=f(x_0)$ and the result in that form $f(x_0)=-\frac{6}{5}$ ? Or is there $f_0(x)$ and not $f(x_0)$

Thanks in advance
• December 21st 2010, 03:58 AM
HallsofIvy
It is $f_0(x)$. Your map, F, is acting on functions, not numbers. A "fixed point" of F is a function, $f_0(x)$ such that $F(f_0)= f_0$. Since $F(f)(x)$ is defined as $\frac{1}{2}f(x)- \frac{3}{5}$ a fixed point is a function $f_0(x)$ such that $\frac{1}{2}f(x)- \frac{3}{5}= f(x)$ for all x. Of course, from that $\frac{1}{2}f(x)= -\frac{3}{5}$ so that the function $f_0$ is defined by $f_0(x)= -\frac{6}{5}$ for all x.
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