Suzuki, Tomonari; Takahashi, Wataru Fixed point theorems and characterizations of metric completeness. (English) Zbl 0902.47050 Topol. Methods Nonlinear Anal. 8, No. 2, 371-382 (1996). While discussing fixed point theorems on complete metric spaces, the authors focus their attention on characterization of metric completeness and derive the following theorems in this connection:(1) Let \(X\) be a metric space. Then \(X\) is complete if and only if every weakly contractive mapping from \(X\) into itself has a fixed point in \(X\);(2) Let \(X\) be a normed linear space and let \(D\) be a convex subset of \(X\). Then \(D\) is complete if and only if every contractive mapping from \(D\) into itself has a fixed point in \(D\). Reviewer: S.K.Chatterjea (Calcutta) Cited in 6 ReviewsCited in 54 Documents MSC: 47H10 Fixed-point theorems 54E50 Complete metric spaces Keywords:fixed point theorems on complete metric spaces; metric completeness; weakly contractive mapping PDFBibTeX XMLCite \textit{T. Suzuki} and \textit{W. Takahashi}, Topol. Methods Nonlinear Anal. 8, No. 2, 371--382 (1996; Zbl 0902.47050) Full Text: DOI