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Math Help - contraction mapping theorem

  1. #1
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    contraction mapping theorem

    I need to show f:[0,1]->[0,1] is a contraction mapping. f(x)=sinx|x^{0.5}-g(x)| where g is continous map form [0,1] to itself

    When I try |f(x)-f(y)|, using triangle inequality and sinx<1, I get it is less that or equal to |x^{0.5}-f(x)|-|y^{0.5}-f(y)| which I can't seem to manipulate (even aware that x,f(x) are in [0,1]) to k|x-y| as required.
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  2. #2
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    Re: contraction mapping theorem

    I require to show that |f(x)-f(y)| is less that or equal to k|x-y| for some 0<k<1
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