The New Hahn Sequence Space via $(p,q)$-Calculus
In this paper, a novel generalized Hahn sequence space, denoted as $h(C(p,q))$, is introduced by utilizing the $(p, q)$-Cesaro matrix. Fundamental properties of this sequence space, such as its completeness and inclusion relations with other well-known sequence spaces, are explored. The duals of thi...
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| Language: | English |
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Emrah Evren KARA
2025-03-01
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| Series: | Communications in Advanced Mathematical Sciences |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/4437583 |
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| author | Serkan Demiriz Sezer Erdem Hacer Bilgin Ellidokuzoğlu |
| author_facet | Serkan Demiriz Sezer Erdem Hacer Bilgin Ellidokuzoğlu |
| author_sort | Serkan Demiriz |
| collection | DOAJ |
| description | In this paper, a novel generalized Hahn sequence space, denoted as $h(C(p,q))$, is introduced by utilizing the $(p, q)$-Cesaro matrix. Fundamental properties of this sequence space, such as its completeness and inclusion relations with other well-known sequence spaces, are explored. The duals of this newly constructed sequence space are also determined, providing insights into its structural and functional characteristics. Furthermore, matrix mapping classes of the form $(h(C(p,q)):\mu)$ are characterized for various classical sequence spaces $\mu \in \{c_0, c, \ell_\infty, \ell_1, h\}$, extending the applicability of the proposed space to broader mathematical contexts. The results obtained contribute to the ongoing development of sequence space theory and its applications in functional analysis. |
| format | Article |
| id | doaj-art-98edfb01f3a84b6cb1517f90ccfa8905 |
| institution | DOAJ |
| issn | 2651-4001 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Emrah Evren KARA |
| record_format | Article |
| series | Communications in Advanced Mathematical Sciences |
| spelling | doaj-art-98edfb01f3a84b6cb1517f90ccfa89052025-08-20T03:14:08ZengEmrah Evren KARACommunications in Advanced Mathematical Sciences2651-40012025-03-0181243510.33434/cams.16008281225The New Hahn Sequence Space via $(p,q)$-CalculusSerkan Demiriz0https://orcid.org/0000-0002-4662-6020Sezer Erdem1https://orcid.org/0000-0001-9420-8264Hacer Bilgin Ellidokuzoğlu2https://orcid.org/0000-0003-1658-201XTOKAT GAZİOSMANPAŞA ÜNİVERSİTESİMALATYA TURGUT ÖZAL ÜNİVERSİTESİRECEP TAYYİP ERDOĞAN ÜNİVERSİTESİ, FEN EDEBİYAT FAKÜLTESİ, MATEMATİKIn this paper, a novel generalized Hahn sequence space, denoted as $h(C(p,q))$, is introduced by utilizing the $(p, q)$-Cesaro matrix. Fundamental properties of this sequence space, such as its completeness and inclusion relations with other well-known sequence spaces, are explored. The duals of this newly constructed sequence space are also determined, providing insights into its structural and functional characteristics. Furthermore, matrix mapping classes of the form $(h(C(p,q)):\mu)$ are characterized for various classical sequence spaces $\mu \in \{c_0, c, \ell_\infty, \ell_1, h\}$, extending the applicability of the proposed space to broader mathematical contexts. The results obtained contribute to the ongoing development of sequence space theory and its applications in functional analysis.https://dergipark.org.tr/en/download/article-file/4437583dualshahn sequence spacematrix mappings(p,q)-calculus(p,q)-cesaro matrix |
| spellingShingle | Serkan Demiriz Sezer Erdem Hacer Bilgin Ellidokuzoğlu The New Hahn Sequence Space via $(p,q)$-Calculus Communications in Advanced Mathematical Sciences duals hahn sequence space matrix mappings (p,q)-calculus (p,q)-cesaro matrix |
| title | The New Hahn Sequence Space via $(p,q)$-Calculus |
| title_full | The New Hahn Sequence Space via $(p,q)$-Calculus |
| title_fullStr | The New Hahn Sequence Space via $(p,q)$-Calculus |
| title_full_unstemmed | The New Hahn Sequence Space via $(p,q)$-Calculus |
| title_short | The New Hahn Sequence Space via $(p,q)$-Calculus |
| title_sort | new hahn sequence space via p q calculus |
| topic | duals hahn sequence space matrix mappings (p,q)-calculus (p,q)-cesaro matrix |
| url | https://dergipark.org.tr/en/download/article-file/4437583 |
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