On statistical A $\mathfrak{A}$ -Cauchy and statistical A $\mathfrak{A}$ -summability via ideal
Abstract The notion of statistical convergence was extended to I $\mathfrak{I}$ -convergence by (Kostyrko et al. in Real Anal. Exch. 26(2):669–686, 2000). In this paper we use such technique and introduce the notion of statistically A I $\mathfrak{A}^{\mathfrak{I}}$ -Cauchy and statistically A I ∗ $...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-02-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-021-02564-4 |
| _version_ | 1828963159071784960 |
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| author | Osama H. H. Edely M. Mursaleen |
| author_facet | Osama H. H. Edely M. Mursaleen |
| author_sort | Osama H. H. Edely |
| collection | DOAJ |
| description | Abstract The notion of statistical convergence was extended to I $\mathfrak{I}$ -convergence by (Kostyrko et al. in Real Anal. Exch. 26(2):669–686, 2000). In this paper we use such technique and introduce the notion of statistically A I $\mathfrak{A}^{\mathfrak{I}}$ -Cauchy and statistically A I ∗ $\mathfrak{A}^{\mathfrak{I}^{\ast }}$ -Cauchy summability via the notion of ideal. We obtain some relations between them and prove that under certain conditions statistical A I $\mathfrak{A}^{\mathfrak{I}}$ -Cauchy and statistical A I ∗ $\mathfrak{A}^{\mathfrak{I}^{\ast }}$ -Cauchy summability are equivalent. Moreover, we give some Tauberian theorems for statistical A I $\mathfrak{A}^{\mathfrak{I}}$ -summability. |
| first_indexed | 2024-12-14T10:20:48Z |
| format | Article |
| id | doaj.art-c0c58a0bd9a947a889ec3d0ddbd5f1a0 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-14T10:20:48Z |
| publishDate | 2021-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-c0c58a0bd9a947a889ec3d0ddbd5f1a02022-12-21T23:06:36ZengSpringerOpenJournal of Inequalities and Applications1029-242X2021-02-012021111110.1186/s13660-021-02564-4On statistical A $\mathfrak{A}$ -Cauchy and statistical A $\mathfrak{A}$ -summability via idealOsama H. H. Edely0M. Mursaleen1Department of Mathematics, Tafila Technical UniversityDepartment of Mathematics, Aligarh Muslim UniversityAbstract The notion of statistical convergence was extended to I $\mathfrak{I}$ -convergence by (Kostyrko et al. in Real Anal. Exch. 26(2):669–686, 2000). In this paper we use such technique and introduce the notion of statistically A I $\mathfrak{A}^{\mathfrak{I}}$ -Cauchy and statistically A I ∗ $\mathfrak{A}^{\mathfrak{I}^{\ast }}$ -Cauchy summability via the notion of ideal. We obtain some relations between them and prove that under certain conditions statistical A I $\mathfrak{A}^{\mathfrak{I}}$ -Cauchy and statistical A I ∗ $\mathfrak{A}^{\mathfrak{I}^{\ast }}$ -Cauchy summability are equivalent. Moreover, we give some Tauberian theorems for statistical A I $\mathfrak{A}^{\mathfrak{I}}$ -summability.https://doi.org/10.1186/s13660-021-02564-4Statistical A I $\mathfrak{A}^{\mathfrak{I}}$ -limit superiorStatistical A I $\mathfrak{A}^{\mathfrak{I}}$ -limit inferiorStatistical A I $\mathfrak{A}^{\mathfrak{I}}$ -boundedStatistical A I $\mathfrak{A}^{\mathfrak{I}}$ -Cauchy summabilityStatistical A I ∗ $\mathfrak{A}^{\mathfrak{I}^{\ast }}$ -Cauchy summabilityTauberian theorem |
| spellingShingle | Osama H. H. Edely M. Mursaleen On statistical A $\mathfrak{A}$ -Cauchy and statistical A $\mathfrak{A}$ -summability via ideal Journal of Inequalities and Applications Statistical A I $\mathfrak{A}^{\mathfrak{I}}$ -limit superior Statistical A I $\mathfrak{A}^{\mathfrak{I}}$ -limit inferior Statistical A I $\mathfrak{A}^{\mathfrak{I}}$ -bounded Statistical A I $\mathfrak{A}^{\mathfrak{I}}$ -Cauchy summability Statistical A I ∗ $\mathfrak{A}^{\mathfrak{I}^{\ast }}$ -Cauchy summability Tauberian theorem |
| title | On statistical A $\mathfrak{A}$ -Cauchy and statistical A $\mathfrak{A}$ -summability via ideal |
| title_full | On statistical A $\mathfrak{A}$ -Cauchy and statistical A $\mathfrak{A}$ -summability via ideal |
| title_fullStr | On statistical A $\mathfrak{A}$ -Cauchy and statistical A $\mathfrak{A}$ -summability via ideal |
| title_full_unstemmed | On statistical A $\mathfrak{A}$ -Cauchy and statistical A $\mathfrak{A}$ -summability via ideal |
| title_short | On statistical A $\mathfrak{A}$ -Cauchy and statistical A $\mathfrak{A}$ -summability via ideal |
| title_sort | on statistical a mathfrak a cauchy and statistical a mathfrak a summability via ideal |
| topic | Statistical A I $\mathfrak{A}^{\mathfrak{I}}$ -limit superior Statistical A I $\mathfrak{A}^{\mathfrak{I}}$ -limit inferior Statistical A I $\mathfrak{A}^{\mathfrak{I}}$ -bounded Statistical A I $\mathfrak{A}^{\mathfrak{I}}$ -Cauchy summability Statistical A I ∗ $\mathfrak{A}^{\mathfrak{I}^{\ast }}$ -Cauchy summability Tauberian theorem |
| url | https://doi.org/10.1186/s13660-021-02564-4 |
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