Tauberian theorems for the product of weighted and Cesàro summability methods for double sequences
In this paper, we obtain necessary and sufficient conditions, under which convergence of a double sequence in Pringsheim's sense follows from its weighted-Cesaro summability. These Tauberian conditions are one-sided or two-sided if it is a sequence of real or complex numbers, respectively.
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Sociedade Brasileira de Matemática
2019-10-01
|
| Series: | Boletim da Sociedade Paranaense de Matemática |
| Online Access: | https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/44135 |
| _version_ | 1797633539030646784 |
|---|---|
| author | Gökşen Fındık İbrahim Çanak |
| author_facet | Gökşen Fındık İbrahim Çanak |
| author_sort | Gökşen Fındık |
| collection | DOAJ |
| description |
In this paper, we obtain necessary and sufficient conditions, under which convergence of a double sequence in Pringsheim's sense follows from its weighted-Cesaro summability. These Tauberian conditions are one-sided or two-sided if it is a sequence of real or complex numbers, respectively.
|
| first_indexed | 2024-03-11T11:55:23Z |
| format | Article |
| id | doaj.art-f45fb5eada1b48489e88227de29ba0e6 |
| institution | Directory Open Access Journal |
| issn | 0037-8712 2175-1188 |
| language | English |
| last_indexed | 2024-03-11T11:55:23Z |
| publishDate | 2019-10-01 |
| publisher | Sociedade Brasileira de Matemática |
| record_format | Article |
| series | Boletim da Sociedade Paranaense de Matemática |
| spelling | doaj.art-f45fb5eada1b48489e88227de29ba0e62023-11-08T20:07:08ZengSociedade Brasileira de MatemáticaBoletim da Sociedade Paranaense de Matemática0037-87122175-11882019-10-0138710.5269/bspm.v38i7.44135Tauberian theorems for the product of weighted and Cesàro summability methods for double sequencesGökşen Fındık0İbrahim Çanak1Ege UniversityEge University In this paper, we obtain necessary and sufficient conditions, under which convergence of a double sequence in Pringsheim's sense follows from its weighted-Cesaro summability. These Tauberian conditions are one-sided or two-sided if it is a sequence of real or complex numbers, respectively. https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/44135 |
| spellingShingle | Gökşen Fındık İbrahim Çanak Tauberian theorems for the product of weighted and Cesàro summability methods for double sequences Boletim da Sociedade Paranaense de Matemática |
| title | Tauberian theorems for the product of weighted and Cesàro summability methods for double sequences |
| title_full | Tauberian theorems for the product of weighted and Cesàro summability methods for double sequences |
| title_fullStr | Tauberian theorems for the product of weighted and Cesàro summability methods for double sequences |
| title_full_unstemmed | Tauberian theorems for the product of weighted and Cesàro summability methods for double sequences |
| title_short | Tauberian theorems for the product of weighted and Cesàro summability methods for double sequences |
| title_sort | tauberian theorems for the product of weighted and cesaro summability methods for double sequences |
| url | https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/44135 |
| work_keys_str_mv | AT goksenfındık tauberiantheoremsfortheproductofweightedandcesarosummabilitymethodsfordoublesequences AT ibrahimcanak tauberiantheoremsfortheproductofweightedandcesarosummabilitymethodsfordoublesequences |