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A comparison of various definitions of contractive mappings


Author: B. E. Rhoades
Journal: Trans. Amer. Math. Soc. 226 (1977), 257-290
MSC: Primary 54H25
DOI: https://doi.org/10.1090/S0002-9947-1977-0433430-4
MathSciNet review: 0433430
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Abstract: A number of authors have defined contractive type mappings on a complete metric space X which are generalizations of the well-known Banach contraction, and which have the property that each such mapping has a unique fixed point. The fixed point can always be found by using Picard iteration, beginning with some initial choice $ {x_0} \in X$. In this paper we compare this multitude of definitions.

X denotes a complete metric space with distance function d, and f a function mapping X into itself.


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DOI: https://doi.org/10.1090/S0002-9947-1977-0433430-4
Article copyright: © Copyright 1977 American Mathematical Society

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