Convergence and well-posedness properties of uniformly locally contractive mappings
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Published:2023-07-16
Issue:
Volume:
Page:1-13
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ISSN:1230-3429
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Container-title:Topological Methods in Nonlinear Analysis
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language:
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Short-container-title:TMNA
Author:
Reich SimeonORCID,
Zaslavski Alexander J.
Abstract
In a 1961 paper by E. Rakotch it was shown that a uniformly locally contractive
mapping has a fixed point. In the present paper we show that for such a mapping,
the fixed point problem is well posed and that inexact iterates of such a mapping
converge to its unique fixed point, uniformly on bounded sets. Using the porosity
notion, we also show that most uniformly locally nonexpansive mappings are, in fact, uniformly locally contractive.
Publisher
Uniwersytet Mikolaja Kopernika/Nicolaus Copernicus University
Subject
Applied Mathematics,Analysis