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Find k

  1. Feb 6, 2008 #1
    how do i find k in the banach fixed point theorem.
    so say i have a function f(x)=1+3x-x^2 in the interval [1,2]
    then how do i find k?

    thank you
     
  2. jcsd
  3. Feb 6, 2008 #2
    It looks to be obvious that that function is a contraction, so apply the definition of a fixed point (k [tex]\in[/tex] [1,2] such that F(k) = k).

    TeX is being weird so I don't know if what I said shows up properly.
     
    Last edited: Feb 6, 2008
  4. Feb 6, 2008 #3
    yes but how do i find that k?
     
  5. Feb 6, 2008 #4
    you know that f(k) = k. It's just algebra. What is f(k)?
     
  6. Feb 6, 2008 #5
    but what do i put as k?
    what value of x isit?
     
  7. Feb 6, 2008 #6

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    k is what you are trying to find! F(k)= 1- 3k- k3 so F(k)= k is just 1- 3k- k2= k. Solve that equation!!!
     
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