On $A$-statistical convergence and $A$-statistical Cauchy via ideal
In [Analysis 1985, 5 (4), 301-313], J.A. Fridy proved an equivalence relation between statistical convergence and statistical Cauchy sequence. In this paper, we define $A^{I^{\ast }}$-statistical convergence and find under certain conditions, that it is equivalent to $A^{I}$-statistical convergence...
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| Format: | Article |
| Language: | English |
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Vasyl Stefanyk Precarpathian National University
2022-12-01
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| Series: | Karpatsʹkì Matematičnì Publìkacìï |
| Subjects: | |
| Online Access: | https://journals.pnu.edu.ua/index.php/cmp/article/view/5052 |
| _version_ | 1827281293124042752 |
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| author | O.H. Edely M. Mursaleen |
| author_facet | O.H. Edely M. Mursaleen |
| author_sort | O.H. Edely |
| collection | DOAJ |
| description | In [Analysis 1985, 5 (4), 301-313], J.A. Fridy proved an equivalence relation between statistical convergence and statistical Cauchy sequence. In this paper, we define $A^{I^{\ast }}$-statistical convergence and find under certain conditions, that it is equivalent to $A^{I}$-statistical convergence defined in [Appl. Math. Lett. 2012, 25 (4), 733-738]. Moreover, we define $A^{I}$- and $A^{I^{\ast }}$-statistical Cauchy sequences and find some equivalent relation with $A^{I}$- and $A^{I^{\ast }}$-statistical convergence. |
| first_indexed | 2024-04-24T08:56:53Z |
| format | Article |
| id | doaj.art-a360c505666f4eee955081d882062f05 |
| institution | Directory Open Access Journal |
| issn | 2075-9827 2313-0210 |
| language | English |
| last_indexed | 2024-04-24T08:56:53Z |
| publishDate | 2022-12-01 |
| publisher | Vasyl Stefanyk Precarpathian National University |
| record_format | Article |
| series | Karpatsʹkì Matematičnì Publìkacìï |
| spelling | doaj.art-a360c505666f4eee955081d882062f052024-04-16T07:12:26ZengVasyl Stefanyk Precarpathian National UniversityKarpatsʹkì Matematičnì Publìkacìï2075-98272313-02102022-12-0114244245210.15330/cmp.14.2.442-4524385On $A$-statistical convergence and $A$-statistical Cauchy via idealO.H. Edely0https://orcid.org/0000-0002-5770-1727M. Mursaleen1Tafila Technical University, P.O.Box 179, Tafila 66110, JordanAligarh Muslim University, Aligarh 202002, India; China Medical University Hospital, China Medical University, Taichung, TaiwanIn [Analysis 1985, 5 (4), 301-313], J.A. Fridy proved an equivalence relation between statistical convergence and statistical Cauchy sequence. In this paper, we define $A^{I^{\ast }}$-statistical convergence and find under certain conditions, that it is equivalent to $A^{I}$-statistical convergence defined in [Appl. Math. Lett. 2012, 25 (4), 733-738]. Moreover, we define $A^{I}$- and $A^{I^{\ast }}$-statistical Cauchy sequences and find some equivalent relation with $A^{I}$- and $A^{I^{\ast }}$-statistical convergence.https://journals.pnu.edu.ua/index.php/cmp/article/view/5052$i$-convergence$a^{i}$-statistical convergence$a^{i^{\ast }}$-statistical convergence$a^{i}$-statistical cauchy convergence$a^{i^{\ast }}$-statistical cauchy convergence |
| spellingShingle | O.H. Edely M. Mursaleen On $A$-statistical convergence and $A$-statistical Cauchy via ideal Karpatsʹkì Matematičnì Publìkacìï $i$-convergence $a^{i}$-statistical convergence $a^{i^{\ast }}$-statistical convergence $a^{i}$-statistical cauchy convergence $a^{i^{\ast }}$-statistical cauchy convergence |
| title | On $A$-statistical convergence and $A$-statistical Cauchy via ideal |
| title_full | On $A$-statistical convergence and $A$-statistical Cauchy via ideal |
| title_fullStr | On $A$-statistical convergence and $A$-statistical Cauchy via ideal |
| title_full_unstemmed | On $A$-statistical convergence and $A$-statistical Cauchy via ideal |
| title_short | On $A$-statistical convergence and $A$-statistical Cauchy via ideal |
| title_sort | on a statistical convergence and a statistical cauchy via ideal |
| topic | $i$-convergence $a^{i}$-statistical convergence $a^{i^{\ast }}$-statistical convergence $a^{i}$-statistical cauchy convergence $a^{i^{\ast }}$-statistical cauchy convergence |
| url | https://journals.pnu.edu.ua/index.php/cmp/article/view/5052 |
| work_keys_str_mv | AT ohedely onastatisticalconvergenceandastatisticalcauchyviaideal AT mmursaleen onastatisticalconvergenceandastatisticalcauchyviaideal |