On Some New Classes of $\mathcal{I}-$Convergent Sequences in GNLS
This paper is devoted to study $\mathcal{I}$-convergent,$\mathcal{I-}$null, $\mathcal{I-}$bounded and bounded sequence spaces in gradual normed linear spaces, denoted by $c_{\| \cdot \|_G} ^\mathcal{I} ,c_{0 \| \cdot \|_G} ^\mathcal{I} ,\ell_{\infty \| \cdot \|_G} ^\mathcal{I}, \ell_{\infty \| \cdot...
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| Format: | Article |
| Language: | English |
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University of Maragheh
2024-03-01
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| Series: | Sahand Communications in Mathematical Analysis |
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| Online Access: | https://scma.maragheh.ac.ir/article_708513_3025356991a645bb55f8cec93b0ab86c.pdf |
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| _version_ | 1823859439378104320 |
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| author | Vakeel Khan Zahid Rahman Ayhan Esi Amit Kumar |
| author_facet | Vakeel Khan Zahid Rahman Ayhan Esi Amit Kumar |
| author_sort | Vakeel Khan |
| collection | DOAJ |
| description | This paper is devoted to study $\mathcal{I}$-convergent,$\mathcal{I-}$null, $\mathcal{I-}$bounded and bounded sequence spaces in gradual normed linear spaces, denoted by $c_{\| \cdot \|_G} ^\mathcal{I} ,c_{0 \| \cdot \|_G} ^\mathcal{I} ,\ell_{\infty \| \cdot \|_G} ^\mathcal{I}, \ell_{\infty \| \cdot\|_G}, m_{\| \cdot \|_G} ^\mathcal{I}$ and $m_{0 \| \cdot \|_G} ^\mathcal{I}$ respectively. We discussed some algebraic and topological properties of these classes. Also, we studied some inclusions involving these spaces. |
| format | Article |
| id | doaj-art-f2de8707ed4f4873972b79b8a37bbc28 |
| institution | Kabale University |
| issn | 2322-5807 2423-3900 |
| language | English |
| publishDate | 2024-03-01 |
| publisher | University of Maragheh |
| record_format | Article |
| series | Sahand Communications in Mathematical Analysis |
| spelling | doaj-art-f2de8707ed4f4873972b79b8a37bbc282025-02-11T05:24:46ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002024-03-01212516710.22130/scma.2023.1999309.1282708513On Some New Classes of $\mathcal{I}-$Convergent Sequences in GNLSVakeel Khan0Zahid Rahman1Ayhan Esi2Amit Kumar3Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India.Department of Mathematics, Faculty of Education, Patia University, Gardez, 2201, Afghanistan.Department of Basic Eng.Sci.(Math.Sect.) Engineering Faculty, Malatya Turgut Ozal University, 44100, Malatya, Turkey.Mathematics, Aligarh Muslim UniversityThis paper is devoted to study $\mathcal{I}$-convergent,$\mathcal{I-}$null, $\mathcal{I-}$bounded and bounded sequence spaces in gradual normed linear spaces, denoted by $c_{\| \cdot \|_G} ^\mathcal{I} ,c_{0 \| \cdot \|_G} ^\mathcal{I} ,\ell_{\infty \| \cdot \|_G} ^\mathcal{I}, \ell_{\infty \| \cdot\|_G}, m_{\| \cdot \|_G} ^\mathcal{I}$ and $m_{0 \| \cdot \|_G} ^\mathcal{I}$ respectively. We discussed some algebraic and topological properties of these classes. Also, we studied some inclusions involving these spaces.https://scma.maragheh.ac.ir/article_708513_3025356991a645bb55f8cec93b0ab86c.pdfgradual normgradual normed liner spacegradually i-convergentgradually i-cauchygradually i-bounded |
| spellingShingle | Vakeel Khan Zahid Rahman Ayhan Esi Amit Kumar On Some New Classes of $\mathcal{I}-$Convergent Sequences in GNLS Sahand Communications in Mathematical Analysis gradual norm gradual normed liner space gradually i-convergent gradually i-cauchy gradually i-bounded |
| title | On Some New Classes of $\mathcal{I}-$Convergent Sequences in GNLS |
| title_full | On Some New Classes of $\mathcal{I}-$Convergent Sequences in GNLS |
| title_fullStr | On Some New Classes of $\mathcal{I}-$Convergent Sequences in GNLS |
| title_full_unstemmed | On Some New Classes of $\mathcal{I}-$Convergent Sequences in GNLS |
| title_short | On Some New Classes of $\mathcal{I}-$Convergent Sequences in GNLS |
| title_sort | on some new classes of mathcal i convergent sequences in gnls |
| topic | gradual norm gradual normed liner space gradually i-convergent gradually i-cauchy gradually i-bounded |
| url | https://scma.maragheh.ac.ir/article_708513_3025356991a645bb55f8cec93b0ab86c.pdf |
| work_keys_str_mv | AT vakeelkhan onsomenewclassesofmathcaliconvergentsequencesingnls AT zahidrahman onsomenewclassesofmathcaliconvergentsequencesingnls AT ayhanesi onsomenewclassesofmathcaliconvergentsequencesingnls AT amitkumar onsomenewclassesofmathcaliconvergentsequencesingnls |