Binomial difference sequence spaces of order m

Abstract

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 ) ) $b^{r,s}_{\infty}(\nabla^{(m)})$ 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.

Keywords

• sequence space
• matrix domain
• Schauder basis
• α-, β- and γ-duals