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 inPascal sequence spaces $p_infty$, $p_c$ and $p_0$, respectively. Furthermore, we determine both γ-,β-, α- duals of newly defined difference sequence spaces of $p_infty$ (∆), $p_c$ (∆) and $p_0$ (∆). Wealso 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.