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Math Help - Fixed point syntax!

  1. #1
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    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
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  2. #2
    MHF Contributor

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    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.
    Last edited by HallsofIvy; December 22nd 2010 at 02:58 AM.
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