On The Difference Sequence Space $l_p(\hat{T}^q)$
| dc.contributor.author | İlkhan, Merve | |
| dc.contributor.author | Alp, Pınar Zengin | |
| dc.date.accessioned | 2025-03-24T19:48:33Z | |
| dc.date.available | 2025-03-24T19:48:33Z | |
| dc.date.issued | 2019 | |
| dc.department | Düzce Üniversitesi | |
| dc.description.abstract | In this study, we introduce a new matrix $\hat{T}^q=(\hat{t}^q_{nk})$ by\[\hat{t}^q_{nk}=\left \{\begin{array}[c]{ccl}%\frac{q_n}{Q_n} t_n & , & k=n\\\frac{q_k}{Q_n}t_k-\frac{q_{k+1}}{Q_n} \frac{1}{t_{k+1}} & , & k<n\\0 & , & k>n .\end{array}\right.\] where $t_k>0$ for all $n\in\mathbb{N}$ and $(t_n)\in c\backslash c_0$. By using the matrix $\hat{T}^q$, we introduce the sequence space $\ell_p(\hat{T}^q)$ for $1\leq p\leq\infty$. In addition, we give some theorems on inclusion relations associated with $\ell_p(\hat{T}^q)$ and find the $\alpha$-, $\beta$-, $\gamma$- duals of this space. Lastly, we analyze the necessary and sufficient conditions for an infinite matrix to be in the classes $(\ell_p(\hat{T}^q),\lambda)$ or $(\lambda,\ell_p(\hat{T}^q))$, where $\lambda\in\{\ell_1,c_0,c,\ell_\infty\}$. | |
| dc.identifier.doi | 10.36753/mathenot.597703 | |
| dc.identifier.endpage | 173 | |
| dc.identifier.issn | 2147-6268 | |
| dc.identifier.issue | 2 | |
| dc.identifier.startpage | 161 | |
| dc.identifier.uri | https://doi.org/10.36753/mathenot.597703 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.12684/19032 | |
| dc.identifier.volume | 7 | |
| dc.language.iso | en | |
| dc.publisher | Murat TOSUN | |
| dc.relation.ispartof | Mathematical Sciences and Applications E-Notes | |
| dc.relation.publicationcategory | Makale - Ulusal Hakemli Dergi - Kurum Öğretim Elemanı | |
| dc.rights | info:eu-repo/semantics/openAccess | |
| dc.snmz | KA_DergiPark_20250324 | |
| dc.subject | sequence spaces|matrix transformations|Schauder basis | |
| dc.title | On The Difference Sequence Space $l_p(\hat{T}^q)$ | |
| dc.type | Article |
