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## On the New Double Binomial Sequence Space

#### Serkan DEMİRİZ [1] , Sezer ERDEM [2]

The aim of this paper is to present the new double Binomial sequence space $\mathcal{B}_{p}^{r,s}$ which consists of all sequences whose double Binomial transforms of orders $r,s$ ($r$ and $s$ are nonzero real numbers with $r+s \neq 0$) are in the space $\mathcal{L}_p$, where $0<p<\infty$. We examine its topological and algebraic properties and inclusion relations. Furthermore, the $\alpha-$, $\beta(bp)-$ and $\gamma-$duals of the space $\mathcal{B}_{p}^{r,s}$ are determined and finally, some 4-dimensional matrix mapping classes related to this space are  characterized.
$\beta(bp)$- and $\gamma$-duals, Double sequence spaces, Binomial matrix, Matrix domain of 4-dimensional matrices, Matrix transformations
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Primary Language en Mathematics Articles Orcid: 0000-0002-4662-6020Author: Serkan DEMİRİZ (Primary Author)Institution: Tokat Gaziosmanpaşa ÜniversitesiCountry: Turkey Orcid: 0000-0001-9420-8264Author: Sezer ERDEMInstitution: TOKAT GAZİOSMANPAŞA ÜNİVERSİTESİCountry: Turkey Publication Date : December 31, 2020
 Bibtex @research article { tjmcs727448, journal = {Turkish Journal of Mathematics and Computer Science}, issn = {}, eissn = {2148-1830}, address = {}, publisher = {Matematikçiler Derneği}, year = {2020}, volume = {12}, pages = {101 - 111}, doi = {10.47000/tjmcs.727448}, title = {On the New Double Binomial Sequence Space}, key = {cite}, author = {Demiriz, Serkan and Erdem, Sezer} } APA Demiriz, S , Erdem, S . (2020). On the New Double Binomial Sequence Space . Turkish Journal of Mathematics and Computer Science , 12 (2) , 101-111 . DOI: 10.47000/tjmcs.727448 MLA Demiriz, S , Erdem, S . "On the New Double Binomial Sequence Space" . Turkish Journal of Mathematics and Computer Science 12 (2020 ): 101-111 Chicago Demiriz, S , Erdem, S . "On the New Double Binomial Sequence Space". Turkish Journal of Mathematics and Computer Science 12 (2020 ): 101-111 RIS TY - JOUR T1 - On the New Double Binomial Sequence Space AU - Serkan Demiriz , Sezer Erdem Y1 - 2020 PY - 2020 N1 - doi: 10.47000/tjmcs.727448 DO - 10.47000/tjmcs.727448 T2 - Turkish Journal of Mathematics and Computer Science JF - Journal JO - JOR SP - 101 EP - 111 VL - 12 IS - 2 SN - -2148-1830 M3 - doi: 10.47000/tjmcs.727448 UR - https://doi.org/10.47000/tjmcs.727448 Y2 - 2020 ER - EndNote %0 Turkish Journal of Mathematics and Computer Science On the New Double Binomial Sequence Space %A Serkan Demiriz , Sezer Erdem %T On the New Double Binomial Sequence Space %D 2020 %J Turkish Journal of Mathematics and Computer Science %P -2148-1830 %V 12 %N 2 %R doi: 10.47000/tjmcs.727448 %U 10.47000/tjmcs.727448 ISNAD Demiriz, Serkan , Erdem, Sezer . "On the New Double Binomial Sequence Space". Turkish Journal of Mathematics and Computer Science 12 / 2 (December 2020): 101-111 . https://doi.org/10.47000/tjmcs.727448 AMA Demiriz S , Erdem S . On the New Double Binomial Sequence Space. TJMCS. 2020; 12(2): 101-111. Vancouver Demiriz S , Erdem S . On the New Double Binomial Sequence Space. Turkish Journal of Mathematics and Computer Science. 2020; 12(2): 101-111. IEEE S. Demiriz and S. Erdem , "On the New Double Binomial Sequence Space", Turkish Journal of Mathematics and Computer Science, vol. 12, no. 2, pp. 101-111, Dec. 2021, doi:10.47000/tjmcs.727448

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