Serkan DEMİRİZ, Sezer ERDEM

On the New Double Binomial Sequence Space

The aim of this paper is to present the new double Binomial sequence space $\mathcal{B}_{p}^{r,s}$ which consists of all sequences whose double Binomial transforms of orders $r,s$ ($r$ and $s$ are nonzero real numbers with $r+s \neq 0$) are in the space $\mathcal{L}_p$, where $0<p<\infty$. We examine its topological and algebraic properties and inclusion relations. Furthermore, the $\alpha-$, $\beta(bp)-$ and $\gamma-$duals of the space $\mathcal{B}_{p}^{r,s}$ are determined and finally, some 4-dimensional matrix mapping classes related to this space are characterized.

Keywords:

$\beta(bp)$- and $\gamma$-duals, Double sequence spaces, Binomial matrix Matrix domain of 4-dimensional matrices, Matrix transformations,

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