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Lipschitz property of norms

  1. Apr 8, 2012 #1
    1. The problem statement, all variables and given/known data
    Hello friends,

    i couldn't find a solution for the question below. Can you help me?

    Thank you very much.

    Let α-norm and β-norm be two different norms on ℝn. Show that f:ℝn->ℝm is Lipschitz in α-norm if and only if it is Lipschitz in β-norm


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Apr 8, 2012 #2

    HallsofIvy

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    You did read the rules for this forum didn't you? And so you know you are required to show your own attempt to solve it?
     
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