Global convergence of the method of successive approximations on \(S^ 1\)
type: Item
instance of: scholarly article
title: Global convergence of the method of successive approximations on \(S^ 1\)
zbMATH Open document ID: 0566.39008
DOI: 10.1016/0022-247X(85)90143-X
author: Giovanni Di Lena
published in: Journal of Mathematical Analysis and Applications
publication date: 1985-01-01T00:00:00Z
review text: Let \(S^ 1\) denote the unit circumference and \(C(S^ 1,S^ 1)\) the class of continuous functions defined in \(S^ 1\) with range in \(S^ 1\). The author considers the recursion defined by \(z_{n+1}=f(z_ n),\) where \(z_ 0\in S^ 1\) and \(f\in C(S^ 1,S^ 1)\). He shows that the sequence \(z_ n\) is convergent for every choice of \(z_ 0\) if and only if (i) f has at least one fixed point, (ii) f has no periodic points of even period.
Mathematics Subject Classification ID: 39B12
Mathematics Subject Classification ID: 26A18
Mathematics Subject Classification ID: 65H05
zbMATH DE Number: 3903216
zbMATH Keywords: recurrence
zbMATH Keywords: recursion
zbMATH Keywords: fixed point
zbMATH Keywords: periodic points
MaRDI profile type: Publication
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full work available at URL: 0022-247x(85)90143-x
OpenAlex ID: W2069768526
description: scientific article; zbMATH DE number 3903216