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

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

Applied Mathematics and Computation, 2015, vol. 268, issue C, 1292-1301

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.

Keywords: Partial quasi-metric; Quasi-metric; Partial metric; Partially ordered set; Complexity analysis; Denotational semantics (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:268:y:2015:i:c:p:1292-1301

DOI: 10.1016/j.amc.2015.06.074

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