1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Show That a Function is Contractive?

  1. May 4, 2007 #1
    1. The problem statement, all variables and given/known data
    Show that the following function is contractive on the indicated intervals. Determine the best values of [lamda] in Equation (2).

    abs(x)^(2/3) on abs(x) < or = 1/3

    2. Relevant equations
    A mapping (or function) F is said to be contractive if there exists a number [lamda] less than 1 such that:

    (Equation (2))
    abs(F(x)-F(y)) < or = [lamda]*abs(x-y)

    for all points x and y in the domain F.

    3. The attempt at a solution
    I'm not really sure what to do with this one or how to get [lamda] in this case.
  2. jcsd
  3. May 4, 2007 #2
    mean value theorem?

    it seems that for the function that is given, such lamda doesn't exist. consider a interval extremely close to 0, let's say
    [tex](-\epsilon, \epsilon)[/tex]

    you see that
    goes to infinity, as it approaches the derivative at 0.

    are you sure you have the correct question?
  4. May 5, 2007 #3
    Thanks for responding, tim_lou. Yes, I'm sure I have the correct question. :) Maybe it's a trick question and it's actually not contractive?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?