Tauberian conditions under which statistical convergence follows from statistical summability $(EC)_{n}^1$
Let $(x_k)$, for $k\in \mathbb{N}\cup \{0\}$ be a sequence of real or complex numbers and set $(EC)_{n}^{1}=\frac{1}{2^n}\sum_{j=0}^{n}{\binom{n}{j}\frac{1}{j+1}\sum_{v=0}^{j}{x_v}},$ $n\in \mathbb{N}\cup \{0\}.$ We present necessary and sufficient conditions, under which $st-\lim_{}{x_k}= L$ foll...
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| Format: | Article |
| Language: | English |
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Sociedade Brasileira de Matemática
2019-10-01
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| Series: | Boletim da Sociedade Paranaense de Matemática |
| Subjects: | |
| Online Access: | http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/32297 |
| _version_ | 1818970018992357376 |
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| author | Naim L. Braha Ismet Temaj |
| author_facet | Naim L. Braha Ismet Temaj |
| author_sort | Naim L. Braha |
| collection | DOAJ |
| description | Let $(x_k)$, for $k\in \mathbb{N}\cup \{0\}$ be a sequence of real or complex numbers and set $(EC)_{n}^{1}=\frac{1}{2^n}\sum_{j=0}^{n}{\binom{n}{j}\frac{1}{j+1}\sum_{v=0}^{j}{x_v}},$ $n\in \mathbb{N}\cup \{0\}.$ We present necessary and sufficient conditions, under which $st-\lim_{}{x_k}= L$ follows from $st-\lim_{}{(EC)_{n}^{1}} = L,$ where L is a finite number. If $(x_k)$ is a sequence of real numbers, then these are one-sided Tauberian conditions. If $(x_k)$ is a sequence of complex numbers, then these are two-sided Tauberian conditions. |
| first_indexed | 2024-12-20T14:29:49Z |
| format | Article |
| id | doaj.art-925647cdf1d349df8b1aedb172027306 |
| institution | Directory Open Access Journal |
| issn | 0037-8712 2175-1188 |
| language | English |
| last_indexed | 2024-12-20T14:29:49Z |
| publishDate | 2019-10-01 |
| publisher | Sociedade Brasileira de Matemática |
| record_format | Article |
| series | Boletim da Sociedade Paranaense de Matemática |
| spelling | doaj.art-925647cdf1d349df8b1aedb1720273062022-12-21T19:37:39ZengSociedade Brasileira de MatemáticaBoletim da Sociedade Paranaense de Matemática0037-87122175-11882019-10-0137491710.5269/bspm.v37i4.3229718043Tauberian conditions under which statistical convergence follows from statistical summability $(EC)_{n}^1$Naim L. Braha0Ismet Temaj1College Vizioni per Arsim Department of Computer Sciences and Applied MathematicsUniversity of Prizren Faculty of EducationLet $(x_k)$, for $k\in \mathbb{N}\cup \{0\}$ be a sequence of real or complex numbers and set $(EC)_{n}^{1}=\frac{1}{2^n}\sum_{j=0}^{n}{\binom{n}{j}\frac{1}{j+1}\sum_{v=0}^{j}{x_v}},$ $n\in \mathbb{N}\cup \{0\}.$ We present necessary and sufficient conditions, under which $st-\lim_{}{x_k}= L$ follows from $st-\lim_{}{(EC)_{n}^{1}} = L,$ where L is a finite number. If $(x_k)$ is a sequence of real numbers, then these are one-sided Tauberian conditions. If $(x_k)$ is a sequence of complex numbers, then these are two-sided Tauberian conditions.http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/32297Statistical convergence$(EC)_{n}^{1}-$ summability$(EC)_{n}^{1}-$ statistically convergentOne-sided and two-sided Tauberian conditions |
| spellingShingle | Naim L. Braha Ismet Temaj Tauberian conditions under which statistical convergence follows from statistical summability $(EC)_{n}^1$ Boletim da Sociedade Paranaense de Matemática Statistical convergence $(EC)_{n}^{1}-$ summability $(EC)_{n}^{1}-$ statistically convergent One-sided and two-sided Tauberian conditions |
| title | Tauberian conditions under which statistical convergence follows from statistical summability $(EC)_{n}^1$ |
| title_full | Tauberian conditions under which statistical convergence follows from statistical summability $(EC)_{n}^1$ |
| title_fullStr | Tauberian conditions under which statistical convergence follows from statistical summability $(EC)_{n}^1$ |
| title_full_unstemmed | Tauberian conditions under which statistical convergence follows from statistical summability $(EC)_{n}^1$ |
| title_short | Tauberian conditions under which statistical convergence follows from statistical summability $(EC)_{n}^1$ |
| title_sort | tauberian conditions under which statistical convergence follows from statistical summability ec n 1 |
| topic | Statistical convergence $(EC)_{n}^{1}-$ summability $(EC)_{n}^{1}-$ statistically convergent One-sided and two-sided Tauberian conditions |
| url | http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/32297 |
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