Convergence rate for a continued fraction expansion related to Fibonacci type sequences
type: Item
instance of: scholarly article
title: Convergence rate for a continued fraction expansion related to Fibonacci type sequences
zbMATH Open document ID: 1227.11094
author: Gabriela Ileana Sebe
published in: Tokyo Journal of Mathematics
publication date: 2011-03-25T00:00:00Z
review text: The author considers some continued fraction expansions related to random Fibonacci-type sequences introduced by \textit{H.-C. Chan} [Fibonacci Q. 44, No. 1, 73--84 (2006; Zbl 1204.11032) and Fibonacci Q. 43, No. 3, 243--255 (2005; Zbl 1081.11010)]. A Wirsing-type approach to the Perron-Frobenius operator of the associated transformation under its invariant measure allows to study the optimality of the convergence rate. Actually, the author obtains upper and lower bounds of the convergence rate which provide a near-optimal solution to the Gauss-Kuzmin-Lévy problem.
reviewed by: Alexey Ustinov
Mathematics Subject Classification ID: 11K50
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 5869977
zbMATH Keywords: continued fractions
zbMATH Keywords: operators on function spaces
zbMATH Keywords: weak limit theorems
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1296483483
OpenAlex ID: W2015886866
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DOI: 10.3836/TJM/1296483483
description: scientific article; zbMATH DE number 5869977