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# Analysis

### International mathematical journal of analysis and its applications

CiteScore 2018: 0.72

SCImago Journal Rank (SJR) 2018: 0.363
Source Normalized Impact per Paper (SNIP) 2018: 0.530

Mathematical Citation Quotient (MCQ) 2018: 0.36

Online
ISSN
2196-6753
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Volume 34, Issue 3

# On ${B}^{\left(m\right)}$-difference sequence spaces using generalized means and compact operators

Amit Maji
/ Parmeshwary Dayal Srivastava
Published Online: 2014-08-01 | DOI: https://doi.org/10.1515/anly-2012-1236

## Abstract.

In this paper, sequence spaces $X\left(r,s,t;{B}^{\left(m\right)}\right)$ for $X\in \left\{{l}_{\infty },c,{c}_{0}\right\}$ are introduced by combining the generalized means and the m-th order generalized difference operator ${B}^{\left(m\right)}\left(u,v\right)$. It is shown that these spaces are complete normed linear spaces and the spaces ${c}_{0}\left(r,s,t;{B}^{\left(m\right)}\right)$, $c\left(r,s,t;{B}^{\left(m\right)}\right)$ have Schauder bases. Furthermore, the α-, β-, γ-duals of these spaces are computed. The necessary and sufficient conditions for some matrix transformations from $X\left(r,s,t;{B}^{\left(m\right)}\right)$ to Y, where $X,Y\in \left\{{l}_{\infty },c,{c}_{0}\right\}$, are also obtained. Finally, some classes of compact operators on the spaces $X\left(r,s,t;{B}^{\left(m\right)}\right)$ for $X\in \left\{{l}_{\infty },c,{c}_{0}\right\}$ are characterized by using the Hausdorff measure of noncompactness.

MSC: 46A45; 46B15; 46B50

Revised: 2014-04-06

Accepted: 2014-05-21

Published Online: 2014-08-01

Published in Print: 2014-08-01

Citation Information: Analysis, Volume 34, Issue 3, Pages 257–281, ISSN (Online) 2196-6753, ISSN (Print) 0174-4747,

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