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Math Help - lifschitz characteristic

  1. #1
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    lifschitz characteristic

    i'm beginner in metric fixed point theory. So i meet a problem to answer the proof of lipschitz characteristic for hilbert spaces is sqrt2. Can you help me?please. i can't find literatures that answer my question. Thanks for your attention.
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  2. #2
    Super Member girdav's Avatar
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    Re: lifschitz characteristic

    Can you recall the definition of Lipschitz characteristic, in order to make your post more self-contained?
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  3. #3
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    Re: lifschitz characteristic

    c' is called lipschitz characteristic for metric space (X,d) if and only if equal to sup{c>=1 : balls in X is c-reguler}.
    Balls in X is c-reguler if and only if for all k<c there exist a,b in (0,1) such that for all x,y elements in X and r>0 with d(x,y)>=(1-a)r,
    there exist z element in X such that (B(x,(1+a)r) meet B(y,k(1+a)r)) in B(z,br).
    Note: B is closed ball in X.
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  4. #4
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    Re: lifschitz characteristic

    if some one can find that lipschitz characteristic >= sqrt2, it's does't matter.... thanks.
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