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## On The Difference Sequence Space $l_p(\hat{T}^q)$

#### Merve İLKHAN [1] , Pınar ZENGİN ALP [2]

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 $\lambda\in\{\ell_1,c_0,c,\ell_\infty\}$.
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Primary Language en Articles Orcid: 0000-0002-0831-1474Author: Merve İLKHAN (Primary Author)Institution: DUZCE UNIVERSITYCountry: Turkey Orcid: 0000-0001-9699-7199Author: Pınar ZENGİN ALP Institution: DUZCE UNIVERSITYCountry: Turkey Publication Date : October 15, 2019  Bibtex @research article { mathenot597703, journal = {Mathematical Sciences and Applications E-Notes}, issn = {}, eissn = {2147-6268}, address = {}, publisher = {Murat TOSUN}, year = {2019}, volume = {7}, pages = {161 - 173}, doi = {10.36753/mathenot.597703}, title = {On The Difference Sequence Space \$l\_p(\\hat\{T\}\^q)\$}, key = {cite}, author = {İLKHAN, Merve and ZENGİN ALP, Pınar} } APA İLKHAN, M , ZENGİN ALP, P . (2019). On The Difference Sequence Space$l_p(\hat{T}^q)$. Mathematical Sciences and Applications E-Notes , 7 (2) , 161-173 . DOI: 10.36753/mathenot.597703 MLA İLKHAN, M , ZENGİN ALP, P . "On The Difference Sequence Space$l_p(\hat{T}^q)$". Mathematical Sciences and Applications E-Notes 7 (2019 ): 161-173 Chicago İLKHAN, M , ZENGİN ALP, P . "On The Difference Sequence Space$l_p(\hat{T}^q)$". Mathematical Sciences and Applications E-Notes 7 (2019 ): 161-173 RIS TY - JOUR T1 - On The Difference Sequence Space$l_p(\hat{T}^q)$AU - Merve İLKHAN , Pınar ZENGİN ALP Y1 - 2019 PY - 2019 N1 - doi: 10.36753/mathenot.597703 DO - 10.36753/mathenot.597703 T2 - Mathematical Sciences and Applications E-Notes JF - Journal JO - JOR SP - 161 EP - 173 VL - 7 IS - 2 SN - -2147-6268 M3 - doi: 10.36753/mathenot.597703 UR - https://doi.org/10.36753/mathenot.597703 Y2 - 2019 ER - EndNote %0 Mathematical Sciences and Applications E-Notes On The Difference Sequence Space$l_p(\hat{T}^q)$%A Merve İLKHAN , Pınar ZENGİN ALP %T On The Difference Sequence Space$l_p(\hat{T}^q)$%D 2019 %J Mathematical Sciences and Applications E-Notes %P -2147-6268 %V 7 %N 2 %R doi: 10.36753/mathenot.597703 %U 10.36753/mathenot.597703 ISNAD İLKHAN, Merve , ZENGİN ALP, Pınar . "On The Difference Sequence Space$l_p(\hat{T}^q)$". Mathematical Sciences and Applications E-Notes 7 / 2 (October 2019): 161-173 . https://doi.org/10.36753/mathenot.597703 AMA İLKHAN M , ZENGİN ALP P . On The Difference Sequence Space$l_p(\hat{T}^q)$. Math. Sci. Appl. E-Notes. 2019; 7(2): 161-173. Vancouver İLKHAN M , ZENGİN ALP P . On The Difference Sequence Space$l_p(\hat{T}^q)\$. Mathematical Sciences and Applications E-Notes. 2019; 7(2): 173-161.

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