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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A generalized Banach contraction principle that characterizes metric completeness


Author: Tomonari Suzuki
Journal: Proc. Amer. Math. Soc. 136 (2008), 1861-1869
MSC (2000): Primary 54H25; Secondary 54E50
Published electronically: December 6, 2007
MathSciNet review: 2373618
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Abstract: We prove a fixed point theorem that is a very simple generalization of the Banach contraction principle and characterizes the metric completeness of the underlying space. We also discuss the Meir-Keeler fixed point theorem.


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Additional Information

Tomonari Suzuki
Affiliation: Department of Mathematics, Kyushu Institute of Technology, Sensuicho, Tobata, Kitakyushu 804-8550, Japan
Email: suzuki-t@mns.kyutech.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09055-7
PII: S 0002-9939(07)09055-7
Keywords: Banach contraction principle, fixed point, metric completeness, Kannan mapping
Received by editor(s): July 17, 2006
Received by editor(s) in revised form: December 18, 2006
Published electronically: December 6, 2007
Additional Notes: The author is supported in part by Grants-in-Aid for Scientific Research from the Japanese Ministry of Education, Culture, Sports, Science and Technology.
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.