On statistical convergence in quasi-metric spaces
A 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 t...
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De Gruyter
2019-06-01
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| Series: | Demonstratio Mathematica |
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| Online Access: | https://doi.org/10.1515/dema-2019-0019 |
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doaj-bb0c5ac117ea4616b1fd3d962c58d7b52021-07-01T05:21:52ZengDe GruyterDemonstratio Mathematica2391-46612019-06-0152122523610.1515/dema-2019-0019dema-2019-0019On statistical convergence in quasi-metric spacesİlkhan Merve0Kara Emrah Evren1Düzce University, Faculty of Arts and Sciences, Department of Mathematics, 81620, Düzce, TurkeyDüzce University, Faculty of Arts and Sciences, Department of Mathematics, 81620, Düzce, TurkeyA 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.https://doi.org/10.1515/dema-2019-0019quasi-metric spaceasymptotic densitystatistical convergenceforward and backward cauchy sequencesp54a0554e5040g15 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
İlkhan Merve Kara Emrah Evren |
| spellingShingle |
İlkhan Merve Kara Emrah Evren On statistical convergence in quasi-metric spaces Demonstratio Mathematica quasi-metric space asymptotic density statistical convergence forward and backward cauchy sequences p54a05 54e50 40g15 |
| author_facet |
İlkhan Merve Kara Emrah Evren |
| author_sort |
İlkhan Merve |
| title |
On statistical convergence in quasi-metric spaces |
| title_short |
On statistical convergence in quasi-metric spaces |
| title_full |
On statistical convergence in quasi-metric spaces |
| title_fullStr |
On statistical convergence in quasi-metric spaces |
| title_full_unstemmed |
On statistical convergence in quasi-metric spaces |
| title_sort |
on statistical convergence in quasi-metric spaces |
| publisher |
De Gruyter |
| series |
Demonstratio Mathematica |
| issn |
2391-4661 |
| publishDate |
2019-06-01 |
| description |
A 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. |
| topic |
quasi-metric space asymptotic density statistical convergence forward and backward cauchy sequences p54a05 54e50 40g15 |
| url |
https://doi.org/10.1515/dema-2019-0019 |
| work_keys_str_mv |
AT ilkhanmerve onstatisticalconvergenceinquasimetricspaces AT karaemrahevren onstatisticalconvergenceinquasimetricspaces |
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1721347319730798592 |