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Partial Metrics Viewed as w -Distances: Extending Some Powerful Fixed-Point Theorems

Author

Listed:
  • Salvador Romaguera

    (Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 Valencia, Spain)

  • Pedro Tirado

    (Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 Valencia, Spain)

Abstract

Involving w -distances and hybrid contractions that combine conditions of the Ćirić type and Samet et al. type, we obtain some general fixed-point results for quasi-metric spaces from which powerful and significant fixed-point theorems on partial metric spaces are deduced as special cases. We present examples showing that our results are real generalizations of those corresponding to the partial metric case and we give an application to the study of recursive equations where the usual Baire partial metric on a domain of words is replaced with a suitable w -distance. Our approach is inspired on the nice fact, stated by Matthews, that every partial metric induces a weighted quasi-metric. Then, we define the notion of a strong w -distance and deduce that every partial metric is a symmetric strong w -distance for its induced weighted quasi-metric space.

Suggested Citation

  • Salvador Romaguera & Pedro Tirado, 2024. "Partial Metrics Viewed as w -Distances: Extending Some Powerful Fixed-Point Theorems," Mathematics, MDPI, vol. 12(24), pages 1-15, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:24:p:3991-:d:1547058
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    References listed on IDEAS

    as
    1. N. Shahzad & O. Valero, 2013. "On 0-Complete Partial Metric Spaces and Quantitative Fixed Point Techniques in Denotational Semantics," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-11, December.
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