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Math Help - if family equicontinuous, prove lipschitz

  1. #1
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    if family equicontinuous, prove lipschitz

    For a function f:R-->R and a>0 set fa(x) = af(x/a). Prove that if the family (fa) a element in (0,infinity) is equicontinuous then f is lipschitz continuous.


    Okay so i started the proof with a def of equicontinuity and am trying to move towards lipschitz but having trouble
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  2. #2
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    Wink

    got to where 0 < a|f(x0/a) -f(x/a)|< epsilon and 0<|x0-x|<delta

    so is a|f(x0/a)-f(x/a)| <= a|x0-x|

    and |f(x0/a)| - |f(x/a)| <= |x0| - |x|

    now what?
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