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Is this a contraction mapping?

  1. Jun 3, 2013 #1
    Hello All:
    I am working on a function given as f(x) = 10/x + (1/20)x^2 for x such that 0≤x≤10. What can be said about the contraction mapping property of f(x)=x?


    If it is not a contraction map, is there any way to make modifications on the function or the interval and prove a contraction mapping result? The upper bound in the interval is important to keep..


    Attempt on problem: I can verify that |f'(x)|≤0.9<1 but I am stuck when it comes to showing that the function maps onto itself in the given interval. It is indeed not true since f(x)→infinity when T=0.

    Thanks very much!!
     
    Last edited: Jun 3, 2013
  2. jcsd
  3. Jun 3, 2013 #2
    Correct me if I'm wrong, but I believe 0≤x≤10 is not a region; 0<x<10 is. You may want to check the problem statement.
     
  4. Jun 3, 2013 #3
    I don't think it will matter but I removed "region". There is no problem statement actually, this is something I am trying to solve for my research.
    Thanks,

     
  5. Jun 3, 2013 #4

    HallsofIvy

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    It is clearly not a contraction map.
    f(1)= 10+ 1/20= 10.05 and f(2)= 5+ 4/20= 5.2
    The distance from 5.2 to 10.05 is definitely NOT less than the distance from 1 to 2.


     
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