Contractive mappings, Kannan mappings and metric completeness

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 h...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 1998-10, Vol.126 (10), p.3117-3124
Main Authors: Shioji, Naoki, Suzuki, Tomonari, Takahashi, Wataru
Format: Article
Language:English
Subjects:
Diagonal lemma
Fixed point property
Mathematical completeness
Mathematical functions
Mathematical theorems
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Summary: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.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-98-04605-X