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A fixed point theorem in partial quasi-metric spaces and an application to Software Engineering

Author

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  • Shahzad, Naseer
  • Valero, Oscar
  • Alghamdi, Mohammed A.
  • Alghamdi, Maryam A.

Abstract

Scott (1970) [11] introduced qualitative fixed point techniques as a suitable mathematical tool for program verification. Inspired by the fact that the Scott mathematical tools do not include metric implements, Matthews (1994) [8] introduced the concept of partial metric space with the aim of reconciling the Scott fixed point techniques with metric spaces and proved a fixed point theorem for self-mappings in partial metric spaces providing, thus, quantitative techniques useful, in the spirit of Scott, in denotational semantics. Schellekens (1995) [10] showed that the original Scott ideas can be also applied to asymptotic complexity analysis of algorithms via quantitative fixed point techniques for self-mappings in quasi-metric spaces. Later on Cerdà-Uguet et al. (2012) [3] showed that, contrarily to the case of Matthews partial metric spaces, partial quasi-metrics are useful for modeling the algorithmic complexity by means of quantitative fixed point techniques that preserve the Scott ideas and Schellekens techniques concurrently.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:268:y:2015:i:c:p:1292-1301
    DOI: 10.1016/j.amc.2015.06.074
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    Cited by:

    1. Le Phuoc Hai & Phan Quoc Khanh & Antoine Soubeyran, 2022. "General Versions of the Ekeland Variational Principle: Ekeland Points and Stop and Go Dynamics," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 347-373, October.
    2. Pilar Fuster-Parra & Javier Martín & Jordi Recasens & Óscar Valero, 2020. "T -Equivalences: The Metric Behavior Revisited," Mathematics, MDPI, vol. 8(4), pages 1-18, April.
    3. 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.

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