Inhomogeneous iterates and nonlinear weak ergodic theorems.
type: Item
instance of: scholarly article
zbMATH Open document ID: 1053.47515
author: Yong-Zhuo Chen
publication date: 2002-09-26T00:00:00Z
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 37A30
Mathematics Subject Classification ID: 47A35
zbMATH DE Number: 1667858
zbMATH Keywords: weakly ergodic sequence
zbMATH Keywords: generalized contraction
MaRDI profile type: Publication
title: Inhomogeneous iterates and nonlinear weak ergodic theorems.
review text: A sequence \(T_n\) of functions defined on a subset \(S\) of a Banach space \(B\) is called weakly ergodic, if for all \(x,y\in S\), NEWLINE\[NEWLINE\lim_{n\to\infty}\,\| T_n\circ\cdots\circ T_1(x)- T_n\circ\cdots\circ T_1(y)\|= 0.NEWLINE\]NEWLINE The author proves several weak ergodic theorems for maps \(T_n\) which leave a certain cone \(S\) invariant and arise from linear operators \(f_n\) by rescaling: \(T_n= {f_n\over\| f_n\|}\).NEWLINENEWLINEFor the entire collection see [Zbl 0969.00060].
reviewed by: Manfred Denker
description: scientific article; zbMATH DE number 1667858