On iterations of Darboux functions
type: Item
instance of: scholarly article
title: On iterations of Darboux functions
zbMATH Open document ID: 0824.26001
author: Tomasz Natkaniec
published in: Real Analysis Exchange
publication date: 1995-05-18T00:00:00Z
review text: Let \(f\) be a function from \(\mathbb{R}\) to \(\mathbb{R}\), let \(A\) be a subset of \(\mathbb{R}\), and let for any \(x\) in \(\mathbb{R}\) there be an \(n\) such that \(f^ n(x)\in A\). Under what conditions \(f\) has a fixed point in \(A\)? The author considers this problem, e.g., for weakly connected or Darboux functions. Also, some examples and open problems are given.
Mathematics Subject Classification ID: 26A18
Mathematics Subject Classification ID: 26A15
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 756679
zbMATH Keywords: weakly connected functions
zbMATH Keywords: iteration
zbMATH Keywords: fixed point
zbMATH Keywords: Darboux functions
reviewed by: Jaroslav Smítal
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 756679