October 29th, 2010, 06:07 PM  #1 
Senior Member Joined: Oct 2009 Posts: 105 Thanks: 0  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.

October 31st, 2010, 07:19 PM  #2 
Senior Member Joined: Oct 2009 Posts: 105 Thanks: 0  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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