Convergence of Infinite Products of Uniformly Locally Nonexpansive Mappings

The generic convergence of infinite products of nonexpansive mappings was established in a 1999 paper of ours. In the present paper, such results are extended to infinite products of uniformly locally nonexpansive mappings. In particular, the convergence of infinite products of uniformly locally con...

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Bibliographic Details
Published in:Mathematics
Main Authors: Simeon Reich, Alexander J. Zaslavski
Format: Article
Language:English
Published: MDPI AG 2025-02-01
Subjects:
complete metric space
fixed point
inexact iterate
infinite product
nonexpansive mapping
Online Access:https://www.mdpi.com/2227-7390/13/5/723
Description
Summary:The generic convergence of infinite products of nonexpansive mappings was established in a 1999 paper of ours. In the present paper, such results are extended to infinite products of uniformly locally nonexpansive mappings. In particular, the convergence of infinite products of uniformly locally contractive mappings, as well as its stability, are proved. Moreover, the Baire category approach and the porosity notion are used to show that most sequences of uniformly locally nonexpansive mappings are, in fact, uniformly locally contractive.
ISSN:2227-7390

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