The Triple Difference Operator of Binomial Poisson Matrix of Fractional

Abstract

In this article we introduce binomial Poisson matrix difference sequence spaces of fractional order $\alpha$, $b_{\Gamma^{3}}^{rs}$ and $b_{\Lambda ^{3}}^{rs}$ by employing fractional difference operator $\Delta^{\alpha}$ defined by \[ \Delta^{\alpha} x_{mnk} = \sum_{u=0}^{\infty} \sum_{v=0}^{\infty} \sum_{w=0}^{\infty} (-1)^{u+v+w} \frac{ \Gamma(\alpha+1)\Gamma(\beta+1)\Gamma(\gamma+1) }{ u!\,v!\,w!\, \Gamma(\alpha-u+1) \Gamma(\beta-v+1) \Gamma(\gamma-w+1) } x_{m-u,n-v,k-w}. \] We give some topological properties, obtain the Schauder basis, and discuss various duals. Finally, we present a graphical interpretation of the operator $B^{rs}(\Delta^{\alpha})$.

Keywords

• Binomial poisson
• difference sequence space
• difference operator $\Delta^{\alpha}$
• Schauder basis

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