A Characterization of Quasi-Metric Completeness in Terms of ? – ? -Contractive Mappings Having Fixed Points

Salvador Romaguera and Pedro Tirado
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Salvador Romaguera: Instituto Universitario de Matemática Pura y Aplicada-IUMPA, Universitat Politècnica de València, 46022 Valencia, Spain
Pedro Tirado: Instituto Universitario de Matemática Pura y Aplicada-IUMPA, Universitat Politècnica de València, 46022 Valencia, Spain

Mathematics, 2019, vol. 8, issue 1, 1-5

Abstract: We obtain a characterization of Hausdorff left K-complete quasi-metric spaces by means of α – ψ -contractive mappings, from which we deduce the somewhat surprising fact that one the main fixed point theorems of Samet, Vetro, and Vetro (see “Fixed point theorems for α – ψ -contractive type mappings”, Nonlinear Anal. 2012 , 75 , 2154–2165), characterizes the metric completeness.

Keywords: fixed point; quasi-metric space; left K-complete; ? – ? -contractive mapping (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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