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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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A comparison of various definitions of contractive mappings
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by B. E. Rhoades
Trans. Amer. Math. Soc. 226 (1977), 257-290
DOI: https://doi.org/10.1090/S0002-9947-1977-0433430-4

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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Bibliographic 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