Binomial difference sequence spaces of fractional order

Abstract

Abstract In this paper, we introduce the sequence spaces b0r,s(∇(α)) $b^{r,s}_{0}( \nabla^{(\alpha)})$, bcr,s(∇(α)) $b^{r,s}_{c}(\nabla^{(\alpha)})$, and b∞r,s(∇(α)) $b^{r,s}_{\infty }(\nabla^{(\alpha)})$. We investigate some functional properties, inclusion relations, and the α-, β-, γ-, and continuous duals of these sets.

Keywords

• Sequence space
• Matrix transformation
• Fractional difference operator
• α-, β-, and γ-duals