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

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 ) ) $b_{c}^{a,b}(B^{(m)})$.

Abstract licence: CC BY-NC-ND

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