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MR1469434 (99a:54023) 54E50 (54H25)
Shioji, Naoki; Suzuki, Tomonari; Takahashi, Wataru Contractive mappings, Kannan mappings and metric completeness. Proc. Amer. Math. Soc. 126 (1998), no. 10, 3117–3124.
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