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Exercises

  1. [16K] Find a function \(f:ℝ→ℝ\) such that

    \[ |f(x)-f(y)|{\lt}|x-y|\quad ∀ x,y∈ℝ \]

    but for which there is no ”fixed point” (that is a point \(x\) for which \(f(x)=x\)=.

    Solution 1

    [16M]

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  • fixed point
  • function, Lipschitz ---
  • function, Hölder ---
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