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

On some binomial B ( m ) $B^{(m)}$ -difference sequence spaces 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 ) ) $b_{c}^{a,b}(B^{(m)})$ . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Inequalities and Applications Springer Journals

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

, Volume 2017 (1) – Aug 22, 2017
11 pages

/lp/springer_journal/on-some-binomial-b-m-b-m-difference-sequence-spaces-8YQAFf0t4C
Publisher
Springer International Publishing
Subject
Mathematics; Analysis; Applications of Mathematics; Mathematics, general
eISSN
1029-242X
D.O.I.
10.1186/s13660-017-1470-4
Publisher site
See Article on Publisher Site

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

### Journal

Journal of Inequalities and ApplicationsSpringer Journals

Published: Aug 22, 2017

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