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October 29th, 2010, 07:07 PM   #1
six
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Contraction Mapping

Anyone have any ideas on finding a contraction mapping in L2 space, leaving the harmonic sequence as a fixed point? There is always the trivial one, that is, every sequence in L2 space mapped to the harmonic sequence. However, I can't think of another example.
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October 31st, 2010, 08:19 PM   #2
six
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Re: Contraction Mapping

Nevermind, I believe I have found a contraction mapping which fixes the harmonic series.

Essentially, this is how my function works...

If the value at the nth term in the sequence is 1/n, then keep it the same. If it is different than 1/n, (call it x_n), then map it to |1/n - x_n|/2.
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