The Abel-type transformations into ℓ
Let t be a sequence in (0,1) that converges to 1, and define the Abel-type matrix Aα,t by ank=(k+α k)tnk+1(1−tn)α+1 for α>−1. The matrix Aα,t determines a sequence-to-sequence variant of the Abel-type power series method of summability introduced by Borwein in [1]. The purpose of this paper i...
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| Format: | Article |
| Language: | English |
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Wiley
1999-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171299227755 |
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| author | Mulatu Lemma |
| author_facet | Mulatu Lemma |
| author_sort | Mulatu Lemma |
| collection | DOAJ |
| description | Let t be a sequence in (0,1) that converges to 1, and define the Abel-type matrix Aα,t by ank=(k+α k)tnk+1(1−tn)α+1 for α>−1. The matrix Aα,t determines a sequence-to-sequence variant of the Abel-type power series method of summability introduced by Borwein in [1]. The purpose of
this paper is to study these matrices as mappings into ℓ.
Necessary and sufficient conditions for Aα,t to be ℓ-ℓ,G-ℓ, and Gw-ℓ are established. Also, the strength of Aα,t in the ℓ-ℓ setting is investigated. |
| format | Article |
| id | doaj-art-9515c62218fd4712841c55f8fb393a45 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1999-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-9515c62218fd4712841c55f8fb393a452025-02-03T06:11:14ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251999-01-0122477578410.1155/S0161171299227755The Abel-type transformations into ℓMulatu Lemma0Department of mathematics, Savannah state university, Savannah, Georgia 31404, USALet t be a sequence in (0,1) that converges to 1, and define the Abel-type matrix Aα,t by ank=(k+α k)tnk+1(1−tn)α+1 for α>−1. The matrix Aα,t determines a sequence-to-sequence variant of the Abel-type power series method of summability introduced by Borwein in [1]. The purpose of this paper is to study these matrices as mappings into ℓ. Necessary and sufficient conditions for Aα,t to be ℓ-ℓ,G-ℓ, and Gw-ℓ are established. Also, the strength of Aα,t in the ℓ-ℓ setting is investigated.http://dx.doi.org/10.1155/S0161171299227755ℓ-ℓ methodsℓ-strongerG-G methodsGw-Gw methods. |
| spellingShingle | Mulatu Lemma The Abel-type transformations into ℓ International Journal of Mathematics and Mathematical Sciences ℓ-ℓ methods ℓ-stronger G-G methods Gw-Gw methods. |
| title | The Abel-type transformations into ℓ |
| title_full | The Abel-type transformations into ℓ |
| title_fullStr | The Abel-type transformations into ℓ |
| title_full_unstemmed | The Abel-type transformations into ℓ |
| title_short | The Abel-type transformations into ℓ |
| title_sort | abel type transformations into l |
| topic | ℓ-ℓ methods ℓ-stronger G-G methods Gw-Gw methods. |
| url | http://dx.doi.org/10.1155/S0161171299227755 |
| work_keys_str_mv | AT mulatulemma theabeltypetransformationsintol AT mulatulemma abeltypetransformationsintol |