Binomial difference sequence spaces of order m - Jian Meng; Meimei Song (Advances in Difference Equations, 2017)
Abstract In this paper, we introduce the binomial sequence spaces b 0 r , s ( ∇ ( m ) ) $b^{r,s}_{0}(\nabla^{(m)})$ , b c r , s ( ∇ ( m ) ) $b^{r,s}_{c}(\nabla^{(m)})$ and b ∞ r , s ( ∇ ( m ) ) $b^{r,s}_{∞}(\nabla^{(m)})$ by combining the binomial transformation and mth order difference operator. We prove the BK-property and some inclusion relations. Also, we obtain the Schauder bases and compute the α-, β- and γ-duals of these sequence spaces.