## A comparison of various definitions of contractive mappings

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- by B. E. Rhoades PDF
- Trans. Amer. Math. Soc.
**226**(1977), 257-290 Request permission

## 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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## Additional Information

- © Copyright 1977 American Mathematical Society
- 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