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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

A development of contraction mapping principles on Hausdorff uniform spaces


Author: Cheng Ming Lee
Journal: Trans. Amer. Math. Soc. 226 (1977), 147-159
MSC: Primary 54H25
DOI: https://doi.org/10.1090/S0002-9947-1977-0428315-3
MathSciNet review: 0428315
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Abstract: Certain generalized Banach's contraction mapping principles on metric spaces are unified and/or extended to Hausdorff uniform spaces. Also given are some relationships between the set of all cluster points of the Picard iterates and the set of all fixed points for the mapping. These are obtained by assuming that the latter set is nonempty and by considering certain ``quasi"-contractive conditions. The ("quasi") contractive conditions are defined by using a suitable family of pseudometrics on the uniform space.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1977-0428315-3
Keywords: Hausdorff uniform space, family of pseudometrics, topology, uniformity, convergence, cluster point, contraction principle, quasi-contraction
Article copyright: © Copyright 1977 American Mathematical Society