On inclusion relations for absolute summability
We obtain necessary and (different) sufficient conditions for a series summable |N¯,pn|k, 1<k≤s<∞, to imply that the series is summable |T|s, where (N¯,pn) is a weighted mean matrix and T is a lower triangular matrix. As corollaries of this result, we obtain several inclusion theorems.
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202012425 |
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doaj-0fd4c3ec46704b06bc72deada4361fdd2020-11-24T22:35:52ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-0132312913810.1155/S0161171202012425On inclusion relations for absolute summabilityB. E. Rhoades0Ekrem Savaş1Department of Mathematics, Indiana University, Bloomington, IN 47405-7106, USADepartment of Mathematics, Yüzüncü Yil University, Van, TurkeyWe obtain necessary and (different) sufficient conditions for a series summable |N¯,pn|k, 1<k≤s<∞, to imply that the series is summable |T|s, where (N¯,pn) is a weighted mean matrix and T is a lower triangular matrix. As corollaries of this result, we obtain several inclusion theorems.http://dx.doi.org/10.1155/S0161171202012425 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
B. E. Rhoades Ekrem Savaş |
| spellingShingle |
B. E. Rhoades Ekrem Savaş On inclusion relations for absolute summability International Journal of Mathematics and Mathematical Sciences |
| author_facet |
B. E. Rhoades Ekrem Savaş |
| author_sort |
B. E. Rhoades |
| title |
On inclusion relations for absolute summability |
| title_short |
On inclusion relations for absolute summability |
| title_full |
On inclusion relations for absolute summability |
| title_fullStr |
On inclusion relations for absolute summability |
| title_full_unstemmed |
On inclusion relations for absolute summability |
| title_sort |
on inclusion relations for absolute summability |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2002-01-01 |
| description |
We obtain necessary
and (different) sufficient conditions for a series summable
|N¯,pn|k, 1<k≤s<∞, to imply that the series is summable |T|s, where (N¯,pn) is a weighted mean matrix and T is a lower triangular matrix. As corollaries of this result, we obtain several inclusion theorems. |
| url |
http://dx.doi.org/10.1155/S0161171202012425 |
| work_keys_str_mv |
AT berhoades oninclusionrelationsforabsolutesummability AT ekremsavas oninclusionrelationsforabsolutesummability |
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1725722635709448192 |