On a class of double difference sequences, their statistical convergence in 2-normed spaces and their duals

Abstract

In this article, we determine a new class of double difference sequence spaces $\ell_2^\infty(\Delta_\nu),$ $c_2(\Delta_\nu)$ and $c_2^0(\Delta_\nu)$ by defining a double difference $\Delta_\nu=(x_{mn}\nu_{mn}- x_{m,n+1}\nu_{m,n+1})-(x_{m+1,n} \nu_{m+1,n}-x_{m+1,n+1}\nu_{m+1,n+1})$, where $\nu=(\nu_{mn})$ is a fixed  double sequence of non zero real numbers satisfying some conditions and $m,n \in \mathbb{N}$,  the set of natural numbers. Moreover, we have studied their various topological properties and certain inclusion relations. We  have also discussed the concept of the statistical convergence of this class in 2-normed space and found their $p\alpha-, p\beta-,p\gamma-$duals.