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Math Help - Continued function?

  1. #1
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    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)
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  2. #2
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    Quote Originally Posted by CaptainBlack View Post
    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.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by halbard View Post
    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
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