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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On contractive mappings


Author: Michael A. Geraghty
Journal: Proc. Amer. Math. Soc. 40 (1973), 604-608
MSC: Primary 54H25
MathSciNet review: 0334176
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Abstract: The Cauchy condition for convergence of a contractive iteration in a complete metric space is replaced by an equivalent functional condition. Many generalizations of the Banach-Neumann contractive mapping principle follow.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0334176-5
Keywords: Contractive mapping, fixed points, convergence of iterations
Article copyright: © Copyright 1973 American Mathematical Society