İlkhan, MerveKara, Emrah Evren2020-04-302020-04-3020190420-12132391-4661https://doi.org/10.1515/dema-2019-0019https://hdl.handle.net/20.500.12684/3923Ilkhan, Merve/0000-0002-0831-1474WOS: 000472069800001A quasi-metric is a distance function which satisfies the triangle inequality but is not symmetric in general. Quasi-metrics are a subject of comprehensive investigation both in pure and applied mathematics in areas such as in functional analysis, topology and computer science. The main purpose of this paper is to extend the convergence and Cauchy conditions in a quasi-metric space by using the notion of asymptotic density. Furthermore, some results obtained are related to completeness, compactness and precompactness in this setting using statistically Cauchy sequences.en10.1515/dema-2019-0019info:eu-repo/semantics/openAccessquasi-metric spaceasymptotic densitystatistical convergenceforward and backward Cauchy sequencesArticle521225236N/A