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Existence of Fixed Points of Suzuki-Type Contractions of Quasi-Metric Spaces

Author

Listed:
  • Basit Ali

    (Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan)

  • Hammad Ali

    (Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan)

  • Talat Nazir

    (Department of Mathematical Sciences, University of South Africa, Florida 0003, South Africa)

  • Zakaria Ali

    (Department of Mathematical Sciences, University of South Africa, Florida 0003, South Africa)

Abstract

In order to generalize classical Banach contraction principle in the setup of quasi-metric spaces, we introduce Suzuki-type contractions of quasi-metric spaces and prove some fixed point results. Further, we suggest a correction in the definition of another class of quasi-metrics known as Δ -symmetric quasi-metrics satisfying a weighted symmetry property. We discuss equivalence of various types of completeness of Δ -symmetric quasi-metric spaces. At the end, we consider the existence of fixed points of generalized Suzuki-type contractions of Δ -symmetric quasi-metric spaces. Some examples have been furnished to make sure that generalizations we obtain are the proper ones.

Suggested Citation

  • Basit Ali & Hammad Ali & Talat Nazir & Zakaria Ali, 2023. "Existence of Fixed Points of Suzuki-Type Contractions of Quasi-Metric Spaces," Mathematics, MDPI, vol. 11(21), pages 1-13, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:21:p:4445-:d:1268269
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    References listed on IDEAS

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    1. Shahzad, Naseer & Valero, Oscar & Alghamdi, Mohammed A. & Alghamdi, Maryam A., 2015. "A fixed point theorem in partial quasi-metric spaces and an application to Software Engineering," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 1292-1301.
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