I have the following mapping (generalized geometric mean):(adsbygoogle = window.adsbygoogle || []).push({});

[tex]y(i)=exp\left[{\sum_j p(j|i)\log x(j)}\right]\\ ,\ i,j=1..N[/tex]

where p(j|i) is a normalized conditional probability.

my question is - is this a contraction mapping?

in other words, does the following equation have a unique solution:

[tex]x(i)=exp\left[{\sum_j p(j|i)\log x(j)}\right]\\ ,\ i,j=1..N[/tex]

thanks in advance,

rubin

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# Contraction map of geometric mean

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