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Contractive mappings, Kannan mappings
and metric completeness

Authors: Naoki Shioji, Tomonari Suzuki and Wataru Takahashi
Journal: Proc. Amer. Math. Soc. 126 (1998), 3117-3124
MSC (1991): Primary 54E50
MathSciNet review: 1469434
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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.

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Additional Information

Naoki Shioji
Affiliation: Faculty of Engineering, Tamagawa University, Tamagawa-Gakuen, Machida, Tokyo 194, Japan

Tomonari Suzuki
Affiliation: Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Ohokayama, Meguro-ku, Tokyo 152, Japan

Wataru Takahashi

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
Article copyright: © Copyright 1998 American Mathematical Society