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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
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.
References:
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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:
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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