Convergence of Infinite Products of Uniformly Locally Nonexpansive Mappings

Simeon Reich () and Alexander J. Zaslavski
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Simeon Reich: Department of Mathematics, The Technion—Israel Institute of Technology, Haifa 32000, Israel
Alexander J. Zaslavski: Department of Mathematics, The Technion—Israel Institute of Technology, Haifa 32000, Israel

Mathematics, 2025, vol. 13, issue 5, 1-12

Abstract: 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.

Keywords: complete metric space; fixed point; inexact iterate; infinite product; nonexpansive mapping (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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