1. Continued function?

I want to solve y=f(y+f(y+f(y+f(y+...)))), where f(x) is some bounded function increasing in x.

First, what is the name of this kind of problem? I know of continued fractions, but here f(x) isn't of the form f(x)=1/(a+x).

Second, how can I find y? (numerically is fine)

2. Originally Posted by CaptainBlack
If this has a solution for a given function f, then:

$y=f(y+f(y))$
Hang on, if $y=f(y+f(y+f(y+f(y+\dots))))$ isn't $y=f(2y)$?

Then all you need to find are the fixed points of the function $g(y)=f(2y)$. This can sometimes be realised by a simple iteration $y_{n+1}=g(y_n)$ for a suitable starting value $y_0$, but you shouldn't rule out the need for more advanced methods.

3. Originally Posted by halbard
Hang on, if $y=f(y+f(y+f(y+f(y+\dots))))$ isn't $y=f(2y)$?

Then all you need to find are the fixed points of the function $g(y)=f(2y)$. This can sometimes be realised by a simple iteration $y_{n+1}=g(y_n)$ for a suitable starting value $y_0$, but you shouldn't rule out the need for more advanced methods.
Yes, now you mention it. That is what I started with but for some reason changed it to what I had posted

CB