English

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

Classical Analysis and ODEs 2017-01-31 v1

Abstract

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.

Keywords

Cite

@article{arxiv.1003.3749,
  title  = {On a fixed point in the metric space of normalized Hausdorff moment sequences},
  author = {Christian Berg and Maryam Beygmohammadi},
  journal= {arXiv preprint arXiv:1003.3749},
  year   = {2017}
}