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Homework Help: Applications with continuity

  1. Sep 30, 2012 #1
    1. The problem statement, all variables and given/known data

    Let f be q function defined from [a,b] to [a,b] such that for every (x,t) in [a,b]^2:

    l f(x)-f(t) l < l x-t l

    1- prove that f is continuous on [a;b]

    2-prove that f accepts a steadfast point in [a,b]

    3. The attempt at a solution
    Should i try to use the definition of a limit to show that f is continuous?
    If not can someone give me headers. Thank you very much
    Last edited: Sep 30, 2012
  2. jcsd
  3. Sep 30, 2012 #2


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    Science Advisor
    Homework Helper
    Gold Member

    Yes, for part 1, use the definition of continuity.

    For part 2, I assume "accepts a steadfast point" means "has a fixed point." If so, consider the function defined by f(x) - x.
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