Convergence of generic infinite products of homogeneous order-preserving mappings
type: Item
instance of: scholarly article
title: Convergence of generic infinite products of homogeneous order-preserving mappings
zbMATH Open document ID: 0972.47044
author: Simeon Reich
author: Alexander J. Zaslavski
published in: Discrete and Continuous Dynamical Systems
publication date: 2000-08-16T00:00:00Z
review text: This article deals with the asymptotic behaviour of (random) products of a generic sequence \(\{A_t\}^\infty_{t=1}\) of homogeneous order-preserving mappings \(A_t\) on a cone \(X_+\) in an ordered Banach space \(X\). The basic results (7 Theorems) are concerned with the existence of a set \({\mathcal F}\) which is a countable intersection of open everywhere dense sets in suitable spaces of sequences, on the one hand, and each element of which has the prescribed asymptotic behaviour together with elements of some neighbourhood, on the other. These results can be considered as modifications of the weak ergodic theorem; some of them state even the convergence of the corresponding infinite products to an operator of type \(f(\cdot)\eta\) where \(f\) is a functional and \(\eta\) a common fixed point of mappings from the considered sequence.
Mathematics Subject Classification ID: 47H07
Mathematics Subject Classification ID: 47H20
zbMATH DE Number: 1492599
zbMATH Keywords: asymptotic behaviour of random products
zbMATH Keywords: ordered Banach space
zbMATH Keywords: weak ergodic theorem
zbMATH Keywords: infinite products
zbMATH Keywords: fixed point
reviewed by: Peter P. Zabreĭko
MaRDI profile type: Publication
full work available at URL: dcds.1999.5.929
OpenAlex ID: W2001834930
DOI: 10.3934/DCDS.1999.5.929
description: scientific article; zbMATH DE number 1492599