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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Salvador Romaguera & Pedro Tirado, 2019. "A Characterization of Quasi-Metric Completeness in Terms of α – ψ -Contractive Mappings Having Fixed Points," Mathematics, MDPI, vol. 8(1), pages 1-5, December.
    • Handle: RePEc:gam:jmathe:v:8:y:2019:i:1:p:16-:d:299964
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