Convergence and well-posedness properties of uniformly locally contractive mappings
DOI:
https://doi.org/10.12775/TMNA.2022.035Keywords
Complete metric space, fixed point, inexact iterate, nonexpansive mappingAbstract
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.References
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