Contractive mappings, Kannan mappings and metric completeness

Shioji, Naoki; Suzuki, Tomonari; Takahashi, Wataru

doi:10.1090/S0002-9939-98-04605-X

Contractive mappings, Kannan mappings and metric completeness
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by Naoki Shioji, Tomonari Suzuki and Wataru Takahashi

Proc. Amer. Math. Soc. 126 (1998), 3117-3124

DOI: https://doi.org/10.1090/S0002-9939-98-04605-X

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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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