On Some New Generalized Difference Sequence Spaces of Non-Absolute Type

Abstract

In this study, we define a new triangle matrix $\hat{W}=\{w_{nk}^{\lambda}(r,s,t)\}$ which derived by using multiplication of $\lambda=(\lambda_{nk})$ triangle matrix with $B(r,s,t)$ triple band matrix. Also, we introduce the sequence spaces $c_{0}^{\lambda}(\hat{B}),c^{\lambda}(\hat{B}),\ell_{\infty}^{\lambda}(\hat{B})$ and $\ell_{p}^{\lambda}(\hat{B})$ by using matrix domain of this matrix on the sequence spaces $c_{0},c,\ell_{\infty}$ and $\ell_{p}$ of the matrix $\hat{W}$, respectively. Moreover, we show that norm isomorphic to the spaces $c_{0},c,\ell_{\infty}$ and $\ell_{p}$, respectively. Furthermore, we establish some inclusion relations concerning with those spaces and determine $\alpha-,\beta-\gamma-$ duals of those spaces and construct their Schauder basis. Finally, we characterize the classes $(\mu_{1}^{\lambda}(\hat{B}):\mu_{2})$ of infinite matrices, where $\mu_{1}\in\{c,c_{0},\ell_{p}\}$ and $\mu_{2}\in\{\ell_{\infty},c,c_{0},\ell_{p}\}$.