On the paranormed binomial sequence spaces

Hacer Bilgin Ellidokuzoğlu; Serkan Demiriz; Ali Köseoğlu

doi:10.32323/ujma.395247

EN

On the paranormed binomial sequence spaces

Abstract

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 $\mu$.

Keywords

Binomial sequence spaces,Paranorm,Matrix domain,Matrix transformations

References

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Hacer Bilgin Ellidokuzoğlu
Türkiye

Serkan Demiriz ^*
Türkiye

Ali Köseoğlu
Türkiye

Publication Date

September 30, 2018

Submission Date

February 15, 2018

Acceptance Date

March 6, 2018

Published in Issue

Year 2018 Volume: 1 Number: 3

DOI

https://doi.org/10.32323/ujma.395247

IZ

https://izlik.org/JA96RK95BZ

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. https://doi.org/10.32323/ujma.395247

AMA

1.Bilgin Ellidokuzoğlu H, Demiriz S, Köseoğlu A. On the paranormed binomial sequence spaces. Univ. J. Math. Appl. 2018;1(3):137-147. doi:10.32323/ujma.395247

Chicago

Bilgin Ellidokuzoğlu, Hacer, Serkan Demiriz, and Ali Köseoğlu. 2018. “On the Paranormed Binomial Sequence Spaces”. Universal Journal of Mathematics and Applications 1 (3): 137-47. https://doi.org/10.32323/ujma.395247.

EndNote

Bilgin Ellidokuzoğlu H, Demiriz S, Köseoğlu A (September 1, 2018) On the paranormed binomial sequence spaces. Universal Journal of Mathematics and Applications 1 3 137–147.

IEEE

[1]H. Bilgin Ellidokuzoğlu, S. Demiriz, and A. Köseoğlu, “On the paranormed binomial sequence spaces”, Univ. J. Math. Appl., vol. 1, no. 3, pp. 137–147, Sept. 2018, doi: 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 1, 2018): 137-147. https://doi.org/10.32323/ujma.395247.

JAMA

1.Bilgin Ellidokuzoğlu H, Demiriz S, Köseoğlu A. On the paranormed binomial sequence spaces. Univ. J. Math. Appl. 2018;1:137–147.

MLA

Bilgin Ellidokuzoğlu, Hacer, et al. “On the Paranormed Binomial Sequence Spaces”. Universal Journal of Mathematics and Applications, vol. 1, no. 3, Sept. 2018, pp. 137-4, doi:10.32323/ujma.395247.

Vancouver

1.Hacer Bilgin Ellidokuzoğlu, Serkan Demiriz, Ali Köseoğlu. On the paranormed binomial sequence spaces. Univ. J. Math. Appl. 2018 Sep. 1;1(3):137-4. doi:10.32323/ujma.395247