The modular sequence space of $\chi^{2}$
In this paper we introduce the modular sequence space of $\chi^{2}$ and examine some topological properties of these space also establish some duals results among them. Lindenstrauss and Tzafriri [7] used the idea of Orlicz function to define the sequence space $\ell_{M}$ which is called an Orlicz s...
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| Format: | Article |
| Language: | English |
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Sociedade Brasileira de Matemática
2014-01-01
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| Series: | Boletim da Sociedade Paranaense de Matemática |
| Subjects: | |
| Online Access: | http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/19385 |
| _version_ | 1819161242331250688 |
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| author | N. Subramanian P. Thirunavukkarasu R. Babu |
| author_facet | N. Subramanian P. Thirunavukkarasu R. Babu |
| author_sort | N. Subramanian |
| collection | DOAJ |
| description | In this paper we introduce the modular sequence space of $\chi^{2}$ and examine some topological properties of these space also establish some duals results among them. Lindenstrauss and Tzafriri [7] used the idea of Orlicz function to define the sequence space $\ell_{M}$ which is called an Orlicz sequence space. Another generalization of Orlicz sequence spaces is due to Woo [9]. We define the sequence spaces $\chi^{2}_{f\lambda}$ and $\chi^{2\lambda}_{g},$ where $f=\left(f_{mn}\right)$ and $g=\left(g_{mn}\right)$ are sequences of modulus functions such that $f_{mn}$ and $g_{mn}$ be mutually complementary for each $m,n.$ |
| first_indexed | 2024-12-22T17:09:14Z |
| format | Article |
| id | doaj.art-b3b198aa308b46a993185c8050ee2eff |
| institution | Directory Open Access Journal |
| issn | 0037-8712 2175-1188 |
| language | English |
| last_indexed | 2024-12-22T17:09:14Z |
| publishDate | 2014-01-01 |
| publisher | Sociedade Brasileira de Matemática |
| record_format | Article |
| series | Boletim da Sociedade Paranaense de Matemática |
| spelling | doaj.art-b3b198aa308b46a993185c8050ee2eff2022-12-21T18:19:06ZengSociedade Brasileira de MatemáticaBoletim da Sociedade Paranaense de Matemática0037-87122175-11882014-01-01321718710.5269/bspm.v32i1.193859300The modular sequence space of $\chi^{2}$N. Subramanian0P. Thirunavukkarasu1R. Babu2SASTRA University Department of MathematicsPeriyar E. V. R. College (Autonomous) P.G. and Research Department of MathematicsShanmugha Polytechnic College Department of MathematicsIn this paper we introduce the modular sequence space of $\chi^{2}$ and examine some topological properties of these space also establish some duals results among them. Lindenstrauss and Tzafriri [7] used the idea of Orlicz function to define the sequence space $\ell_{M}$ which is called an Orlicz sequence space. Another generalization of Orlicz sequence spaces is due to Woo [9]. We define the sequence spaces $\chi^{2}_{f\lambda}$ and $\chi^{2\lambda}_{g},$ where $f=\left(f_{mn}\right)$ and $g=\left(g_{mn}\right)$ are sequences of modulus functions such that $f_{mn}$ and $g_{mn}$ be mutually complementary for each $m,n.$http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/19385analytic sequencemodulus functiondouble sequences$\chi^{2}$ spacemodularduals |
| spellingShingle | N. Subramanian P. Thirunavukkarasu R. Babu The modular sequence space of $\chi^{2}$ Boletim da Sociedade Paranaense de Matemática analytic sequence modulus function double sequences $\chi^{2}$ space modular duals |
| title | The modular sequence space of $\chi^{2}$ |
| title_full | The modular sequence space of $\chi^{2}$ |
| title_fullStr | The modular sequence space of $\chi^{2}$ |
| title_full_unstemmed | The modular sequence space of $\chi^{2}$ |
| title_short | The modular sequence space of $\chi^{2}$ |
| title_sort | modular sequence space of chi 2 |
| topic | analytic sequence modulus function double sequences $\chi^{2}$ space modular duals |
| url | http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/19385 |
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