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Contractive mappings, Kannan mappings and metric completeness
Author(s):
Naoki
Shioji;
Tomonari
Suzuki;
Wataru
Takahashi
Journal:
Proc. Amer. Math. Soc.
126
(1998),
3117-3124.
MSC (1991):
Primary 54E50
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Abstract:
In this paper, we first study the relationship between weakly contractive mappings and weakly Kannan mappings. Further, we discuss characterizations of metric completeness which are connected with the existence of fixed points for mappings. Especially, we show that a metric space is complete if it has the fixed point property for Kannan mappings.
References:
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Additional Information:
Naoki
Shioji
Affiliation:
Faculty of Engineering, Tamagawa University, Tamagawa-Gakuen, Machida, Tokyo 194, Japan
Email:
shioji@eng.tamagawa.ac.jp
Tomonari
Suzuki
Affiliation:
Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Ohokayama, Meguro-ku, Tokyo 152, Japan
Email:
tomonari@is.titech.ac.jp
Wataru
Takahashi
Email:
wataru@is.titech.ac.jp
DOI:
10.1090/S0002-9939-98-04605-X
PII:
S 0002-9939(98)04605-X
Keywords:
Completeness,
contractive mapping,
Kannan mapping,
fixed point,
mean
Received by editor(s):
October 25, 1996
Received by editor(s) in revised form:
February 27, 1997
Communicated by:
Palle E. T. Jorgensen
Copyright of article:
Copyright
1998,
American Mathematical Society
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