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

Merve İlkhan; Pınar Zengin Alp

doi:10.36753/mathenot.597703

EN

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

Abstract

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 $\lambda\in\{\ell_1,c_0,c,\ell_\infty\}$.

Keywords

sequence spaces,matrix transformations,Schauder basis,$\alpha- \beta- \gamma-duals

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Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Merve İlkhan ^*
0000-0002-0831-1474
Türkiye

Pınar Zengin Alp
0000-0001-9699-7199
Türkiye

Publication Date

October 15, 2019

Submission Date

July 28, 2019

Acceptance Date

August 16, 2019

Published in Issue

Year 2019 Volume: 7 Number: 2

DOI

https://doi.org/10.36753/mathenot.597703

IZ

https://izlik.org/JA25TW72WK

APA

İlkhan, M., & Zengin Alp, P. (2019). On The Difference Sequence Space $l_p(\hat{T}^q)$. Mathematical Sciences and Applications E-Notes, 7(2), 161-173. https://doi.org/10.36753/mathenot.597703

AMA

1.İlkhan M, Zengin Alp P. On The Difference Sequence Space $l_p(\hat{T}^q)$. Math. Sci. Appl. E-Notes. 2019;7(2):161-173. doi:10.36753/mathenot.597703

Chicago

İlkhan, Merve, and Pınar Zengin Alp. 2019. “On The Difference Sequence Space $l_p(\hat{T}^q)$”. Mathematical Sciences and Applications E-Notes 7 (2): 161-73. https://doi.org/10.36753/mathenot.597703.

EndNote

İlkhan M, Zengin Alp P (October 1, 2019) On The Difference Sequence Space $l_p(\hat{T}^q)$. Mathematical Sciences and Applications E-Notes 7 2 161–173.

IEEE

[1]M. İlkhan and P. Zengin Alp, “On The Difference Sequence Space $l_p(\hat{T}^q)$”, Math. Sci. Appl. E-Notes, vol. 7, no. 2, pp. 161–173, Oct. 2019, doi: 10.36753/mathenot.597703.

ISNAD

İlkhan, Merve - Zengin Alp, Pınar. “On The Difference Sequence Space $l_p(\hat{T}^q)$”. Mathematical Sciences and Applications E-Notes 7/2 (October 1, 2019): 161-173. https://doi.org/10.36753/mathenot.597703.

JAMA

1.İlkhan M, Zengin Alp P. On The Difference Sequence Space $l_p(\hat{T}^q)$. Math. Sci. Appl. E-Notes. 2019;7:161–173.

MLA

İlkhan, Merve, and Pınar Zengin Alp. “On The Difference Sequence Space $l_p(\hat{T}^q)$”. Mathematical Sciences and Applications E-Notes, vol. 7, no. 2, Oct. 2019, pp. 161-73, doi:10.36753/mathenot.597703.

Vancouver

1.Merve İlkhan, Pınar Zengin Alp. On The Difference Sequence Space $l_p(\hat{T}^q)$. Math. Sci. Appl. E-Notes. 2019 Oct. 1;7(2):161-73. doi:10.36753/mathenot.597703