TY  - JOUR
T1  - On the paranormed binomial sequence spaces
AU  - Demiriz, Serkan
AU  - Bilgin Ellidokuzoğlu, Hacer
AU  - Köseoğlu, Ali
PY  - 2018
DA  - September
Y2  - 2018
DO  - 10.32323/ujma.395247
JF  - Universal Journal of Mathematics and Applications
JO  - Univ. J. Math. Appl.
PB  - Emrah Evren KARA
WT  - DergiPark
SN  - 2619-9653
SP  - 137
EP  - 147
VL  - 1
IS  - 3
LA  - en
AB  - 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 $\mu$.
KW  - Binomial sequence spaces
KW  - Paranorm
KW  - Matrix domain
KW  - Matrix transformations
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UR  - https://doi.org/10.32323/ujma.395247
L1  - https://dergipark.org.tr/en/download/article-file/542396
ER  -