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Math Help - fixed points

  1. #1
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    fixed points

    Let f:[a,b] --> R be continous on [a,b] and differentiable on (a,b). Suppose that abs( f'(x) ) is less than 1 for all x in (a,b). Prove that f has at most one fixed point.
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  2. #2
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    Quote Originally Posted by friday616 View Post
    Let f:[a,b] --> R be continous on [a,b] and differentiable on (a,b). Suppose that abs( f'(x) ) is less than 1 for all x in (a,b). Prove that f has at most one fixed point.

    Suppose \alpha\,,\beta \in (a,b) are two fixed point of f(x). Apply now Rolle's theorem for f(x) in the interval [\alpha,\beta] and get a contradiction.

    Tonio
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