1. Limited time only! Sign up for a free 30min personal 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!

Help interpreting HW question on Lipschitz Hölder

  1. Sep 9, 2012 #1
    1. The problem statement, all variables and given/known data
    I only need help interpreting the following:
    Show that every Lipschitz continuous function is α-Hölder continuous for
    every α ∈ (0, 1
    The definition of both is given in the homework so this seems trivial but it's a graduate level class. Am I mising something? Thanks for any help!

    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 9, 2012 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Well, what are those definitions? Why do you say this is "trivial"?
     
  4. Sep 9, 2012 #3
    Well by the definitions, Lipschitz is a special case of α-Hölder when α=1. Since α is contained in the interval (0,1] (which is the interval given for α-Hölder) then by def. every Lipschitz continuous function is α-Hölder continuous.
     
  5. Sep 9, 2012 #4
    Your question asked to show that it is α-Hölder continuous for every α ∈ (0, 1], not just for α=1. Unless this was a typo? Yes, Lipschitz implies Hölder of order 1. But does it imply this for all orders less than 1?
     
  6. Sep 9, 2012 #5
    Ahhh, great! yes your right I see it now. Funny how sometimes one can not see what is right in front of them. Thanks for the help, that's exactly what I needed.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Help interpreting HW question on Lipschitz Hölder
Loading...