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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Path stability and nonlinear weak ergodic theorems


Author: Yong-Zhuo Chen
Journal: Trans. Amer. Math. Soc. 352 (2000), 5279-5292
MSC (2000): Primary 47H07, 47H09; Secondary 47H10
Published electronically: July 12, 2000
MathSciNet review: 1707493
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $\{f_{n} \}$ be a sequence of nonlinear operators. We discuss the asymptotic properties of their inhomogeneous iterates $f_{n} \circ f_{n-1} \circ \cdots \circ f_{1}\,$ in metric spaces, then apply the results to the ordered Banach spaces through projective metrics. Theorems on path stability and nonlinear weak ergodicity are obtained in this paper.


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Additional Information

Yong-Zhuo Chen
Affiliation: Division of Natural Sciences, University of Pittsburgh at Bradford, Bradford, Pennsylvania 16701
Email: yong@imap.pitt.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02600-3
PII: S 0002-9947(00)02600-3
Keywords: Hilbert metric, inhomogeneous iterates, metric space, monotone operator, ordered Banach space, Thompson's metric
Received by editor(s): June 30, 1998
Received by editor(s) in revised form: June 1, 1999
Published electronically: July 12, 2000
Article copyright: © Copyright 2000 American Mathematical Society