On statistical convergence in quasi-metric spaces

• Autorzy: İlkhan Merve , Kara Emrah Evren

Identyfikatory

DOI

10.1515/dema-2019-0019

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

quasi-metric space; asymptotic density; statistical convergence; forward Cauchy sequences; backward Cauchy sequences

PL

przestrzeń quasi-metryczna; gęstość asymptotyczna; zbieżność statystyczna; ciąg Cauchy'ego

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2019
• Tom: Vol. 52, nr 1
• Strony: 225--236
• Opis fizyczny: Bibliogr. 34 poz.

Twórcy

autor

İlkhan Merve

• Düzce University, Faculty of Arts and Sciences, Department of Mathematics, 81620, Düzce, Turkey

autor

Kara Emrah Evren

• Düzce University, Faculty of Arts and Sciences, Department of Mathematics, 81620, Düzce, Turkey

Bibliografia

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Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).