# On a fixed point in the metric space of normalized Hausdorff moment sequences

@article{Berg2010OnAF, title={On a fixed point in the metric space of normalized Hausdorff moment sequences}, author={Christian Berg and Maryam Beygmohammadi}, journal={arXiv: Classical Analysis and ODEs}, year={2010} }

We show that the transformation (x_n)_{n\ge 1}\to (1/(1+x_1+...+x_n))_{n\ge 1} of the compact set of sequences (x_n)_{n\ge 1} of numbers from the unit interval [0,1] has a unique fixed point, which is attractive. The fixed point turns out to be a Hausdorff moment sequence studied in papers by Berg and Dur\'an in 2008.

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