Year 2018, Volume 1 , Issue 3, Pages 137 - 147 2018-09-30

On the paranormed binomial sequence spaces

Hacer Bilgin Ellidokuzoğlu [1] , Serkan Demiriz [2] , Ali Köseoğlu [3]


In this paper the sequence spaces $b_0^{r,s}(p)$, $b_c^{r,s}(p)$, $b_{\infty}^{r,s}(p)$ and $b^{r,s}(p)$ which are the generalization of the classical Maddox's paranormed sequence spaces have been introduced and proved that the spaces $b_0^{r,s}(p)$, $b_c^{r,s}(p)$, $b_{\infty}^{r,s}(p)$ and $b^{r,s}(p)$ are linearly isomorphic to spaces $c_0(p)$, $c(p)$, $\ell_{\infty}(p)$ and $\ell(p)$, respectively. Besides this, the $\alpha-,\beta-$ and $\gamma-$duals of the spaces $b_0^{r,s}(p)$, $b_c^{r,s}(p)$, and $b^{r,s}(p)$ have been computed, their bases have been constructed and some topological properties of these spaces have been studied. Finally, the classes of matrices $(b_0^{r,s}(p) : \mu)$, $(b^{r,s}_c(p): \mu)$ and $(b^{r,s}(p): \mu)$ have been characterized, where $\mu$ is one of the sequence spaces $\ell_\infty,c$ and $c_0$ and derives the other characterizations for the special cases of $\mu$.

Binomial sequence spaces, Paranorm, Matrix domain, Matrix transformations
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Primary Language en
Subjects Mathematics
Journal Section Articles
Authors

Author: Hacer Bilgin Ellidokuzoğlu
Country: Turkey


Author: Serkan Demiriz (Primary Author)
Country: Turkey


Author: Ali Köseoğlu
Country: Turkey


Dates

Publication Date : September 30, 2018

Bibtex @research article { ujma395247, journal = {Universal Journal of Mathematics and Applications}, issn = {2619-9653}, address = {}, publisher = {Emrah Evren KARA}, year = {2018}, volume = {1}, pages = {137 - 147}, doi = {10.32323/ujma.395247}, title = {On the paranormed binomial sequence spaces}, key = {cite}, author = {Bilgin Ellidokuzoğlu, Hacer and Demiriz, Serkan and Köseoğlu, Ali} }
APA Bilgin Ellidokuzoğlu, H , Demiriz, S , Köseoğlu, A . (2018). On the paranormed binomial sequence spaces. Universal Journal of Mathematics and Applications , 1 (3) , 137-147 . DOI: 10.32323/ujma.395247
MLA Bilgin Ellidokuzoğlu, H , Demiriz, S , Köseoğlu, A . "On the paranormed binomial sequence spaces". Universal Journal of Mathematics and Applications 1 (2018 ): 137-147 <https://dergipark.org.tr/en/pub/ujma/issue/39345/395247>
Chicago Bilgin Ellidokuzoğlu, H , Demiriz, S , Köseoğlu, A . "On the paranormed binomial sequence spaces". Universal Journal of Mathematics and Applications 1 (2018 ): 137-147
RIS TY - JOUR T1 - On the paranormed binomial sequence spaces AU - Hacer Bilgin Ellidokuzoğlu , Serkan Demiriz , Ali Köseoğlu Y1 - 2018 PY - 2018 N1 - doi: 10.32323/ujma.395247 DO - 10.32323/ujma.395247 T2 - Universal Journal of Mathematics and Applications JF - Journal JO - JOR SP - 137 EP - 147 VL - 1 IS - 3 SN - 2619-9653- M3 - doi: 10.32323/ujma.395247 UR - https://doi.org/10.32323/ujma.395247 Y2 - 2018 ER -
EndNote %0 Universal Journal of Mathematics and Applications On the paranormed binomial sequence spaces %A Hacer Bilgin Ellidokuzoğlu , Serkan Demiriz , Ali Köseoğlu %T On the paranormed binomial sequence spaces %D 2018 %J Universal Journal of Mathematics and Applications %P 2619-9653- %V 1 %N 3 %R doi: 10.32323/ujma.395247 %U 10.32323/ujma.395247
ISNAD Bilgin Ellidokuzoğlu, Hacer , Demiriz, Serkan , Köseoğlu, Ali . "On the paranormed binomial sequence spaces". Universal Journal of Mathematics and Applications 1 / 3 (September 2018): 137-147 . https://doi.org/10.32323/ujma.395247
AMA Bilgin Ellidokuzoğlu H , Demiriz S , Köseoğlu A . On the paranormed binomial sequence spaces. Univ. J. Math. Appl.. 2018; 1(3): 137-147.
Vancouver Bilgin Ellidokuzoğlu H , Demiriz S , Köseoğlu A . On the paranormed binomial sequence spaces. Universal Journal of Mathematics and Applications. 2018; 1(3): 147-137.