Özet:

In this study, we introduce a new matrix $\hat{T}^q=(\hat{t}^q_{nk})$ by \[ \hat{t}^q_{nk}=\left \{ \begin{array} [c]{ccl}% \frac{q_n}{Q_n} t_n & , & k=n\\ \frac{q_k}{Q_n}t_k-\frac{q_{k+1}}{Q_n} \frac{1}{t_{k+1}} & , & kn . \end{array} \right. \] 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 $\lambda\in\{\ell_1,c_0,c,\ell_\infty\}$.

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