Difference Sequence Spaces Derived by using Pascal Transform

Abstract

The essential goal of this manuscript is to investigate some novel sequence spaces of $p_\infty$ (?), $p_c$ (?) and $p_0$ (?) which are comprised by all sequence spaces whose differences are in Pascal sequence spaces $p_\infty$, $p_c$ and $p_0$, respectively. Furthermore, we determine both ?-, ?-, ?- duals of newly defined difference sequence spaces of $p_\infty$ (?), $p_c$ (?) and $p_0$ (?). We also obtain bases of the newly defined difference sequence spaces of $p_c$ (?) and $p_0$ (?). Finally, necessary and sufficient conditions on an infinite matrix belonging to the classes ($p_c$ (?) : $\iota_\infty$ ) and ($p_c$ (?) : c) are characterized.