On The Difference Sequence Space $l_p(\hat{T}^q)$
Küçük Resim Yok
Tarih
2019
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Murat TOSUN
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
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 $\lambda\in\{\ell_1,c_0,c,\ell_\infty\}$.
Açıklama
Anahtar Kelimeler
sequence spaces|matrix transformations|Schauder basis
Kaynak
Mathematical Sciences and Applications E-Notes
WoS Q Değeri
Scopus Q Değeri
Cilt
7
Sayı
2
