Proceedings of the American Mathematical Society

A generalized Banach contraction principle that characterizes metric completeness

Author(s): Tomonari Suzuki
Journal: Proc. Amer. Math. Soc. 136 (2008), 1861-1869.
MSC (2000): Primary 54H25; Secondary 54E50
Posted: December 6, 2007
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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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 54H25, 54E50

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

DOI: 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
Posted: 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
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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