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 ${\mu }_2\in \{{\ell }_{\infty },c,c_0,{\ell }_p\}$.

31 pages