Thread: 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)

Originally Posted by CaptainBlack

If this has a solution for a given function f, then:

Hang on, if isn't ?

Then all you need to find are the fixed points of the function . This can sometimes be realised by a simple iteration for a suitable starting value , but you shouldn't rule out the need for more advanced methods.

Originally Posted by halbard

Hang on, if isn't ?

Then all you need to find are the fixed points of the function . This can sometimes be realised by a simple iteration for a suitable starting value , 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