On some binomial B ( m ) $B^{(m)}$ -difference sequence spaces

Abstract

Abstract In this paper, we introduce the binomial sequence spaces b 0 a , b ( B ( m ) ) $b^{a,b}_{0}(B^{(m)})$ , b c a , b ( B ( m ) ) $b^{a,b}_{c}(B^{(m)})$ and b ∞ a , b ( B ( m ) ) $b^{a,b}_{\infty}(B^{(m)})$ by combining the binomial transformation and difference operator. We prove the BK-property and some inclusion relations. Furthermore, we obtain Schauder bases and compute the α-, β- and γ-duals of these sequence spaces. Finally, we characterize matrix transformations on the sequence space b c a , b ( B ( m ) ) $b_{c}^{a,b}(B^{(m)})$ .

Keywords

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