  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
$\mu_{2}\in\{\ell_{\infty},c,c_{0},\ell_{p}\}$.
