Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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



A comparison of various definitions of contractive mappings

Author: B. E. Rhoades
Journal: Trans. Amer. Math. Soc. 226 (1977), 257-290
MSC: Primary 54H25
MathSciNet review: 0433430
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 54H25

Retrieve articles in all journals with MSC: 54H25

Additional Information

Article copyright: © Copyright 1977 American Mathematical Society