On the New Double Binomial Sequence Space

Year 2020, Volume: 12 Issue: 2, 101 - 111, 31.12.2020

Serkan Demiriz Sezer Erdem

https://doi.org/10.47000/tjmcs.727448

Cited By: 3

Abstract

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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