A Characterization of Completeness via Absolutely Convergent Series and the Weierstrass Test in Asymmetric Normed Semilinear Spaces
Asymmetric normed semilinear spaces are studied. A description of biBanach, left K-sequentially complete, and Smyth complete asymmetric normed semilinear spaces is provided and three appropriate notions of absolute convergence in the asymmetric normed framework are introduced. Some characterizations...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/596384 |
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| author | N. Shahzad O. Valero |
| author_facet | N. Shahzad O. Valero |
| author_sort | N. Shahzad |
| collection | DOAJ |
| description | Asymmetric normed semilinear spaces are studied. A description of biBanach, left K-sequentially complete, and Smyth complete asymmetric normed semilinear spaces is provided and three appropriate notions of absolute convergence in the asymmetric normed framework are introduced. Some characterizations of completeness are also obtained via absolutely convergent series. Moreover, as an application, a Weierstrass test for the convergence of series is derived. |
| format | Article |
| id | doaj-art-c0ff3868df9f488bbbfd9df9b718515f |
| institution | DOAJ |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-c0ff3868df9f488bbbfd9df9b718515f2025-08-20T03:23:24ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/596384596384A Characterization of Completeness via Absolutely Convergent Series and the Weierstrass Test in Asymmetric Normed Semilinear SpacesN. Shahzad0O. Valero1Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21859, Saudi ArabiaDepartamento de Ciencias Matemáticas e Informática, Universidad de las Islas Baleares, Carretera de Valldemossa km. 7.5, 07122 Palma de Mallorca, SpainAsymmetric normed semilinear spaces are studied. A description of biBanach, left K-sequentially complete, and Smyth complete asymmetric normed semilinear spaces is provided and three appropriate notions of absolute convergence in the asymmetric normed framework are introduced. Some characterizations of completeness are also obtained via absolutely convergent series. Moreover, as an application, a Weierstrass test for the convergence of series is derived.http://dx.doi.org/10.1155/2014/596384 |
| spellingShingle | N. Shahzad O. Valero A Characterization of Completeness via Absolutely Convergent Series and the Weierstrass Test in Asymmetric Normed Semilinear Spaces Abstract and Applied Analysis |
| title | A Characterization of Completeness via Absolutely Convergent Series and the Weierstrass Test in Asymmetric Normed Semilinear Spaces |
| title_full | A Characterization of Completeness via Absolutely Convergent Series and the Weierstrass Test in Asymmetric Normed Semilinear Spaces |
| title_fullStr | A Characterization of Completeness via Absolutely Convergent Series and the Weierstrass Test in Asymmetric Normed Semilinear Spaces |
| title_full_unstemmed | A Characterization of Completeness via Absolutely Convergent Series and the Weierstrass Test in Asymmetric Normed Semilinear Spaces |
| title_short | A Characterization of Completeness via Absolutely Convergent Series and the Weierstrass Test in Asymmetric Normed Semilinear Spaces |
| title_sort | characterization of completeness via absolutely convergent series and the weierstrass test in asymmetric normed semilinear spaces |
| url | http://dx.doi.org/10.1155/2014/596384 |
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