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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

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Volume 34, Issue 3


On B(m)-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


In this paper, sequence spaces X(r,s,t;B(m)) for X{l,c,c0} are introduced by combining the generalized means and the m-th order generalized difference operator B(m)(u,v). It is shown that these spaces are complete normed linear spaces and the spaces c0(r,s,t;B(m)), c(r,s,t;B(m)) 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(r,s,t;B(m)) to Y, where X,Y{l,c,c0}, are also obtained. Finally, some classes of compact operators on the spaces X(r,s,t;B(m)) for X{l,c,c0} are characterized by using the Hausdorff measure of noncompactness.

Keywords: Difference operator; generalized means; matrix transformation; Hausdorff measure of noncompactness; compact operators

MSC: 46A45; 46B15; 46B50

About the article

Received: 2013-11-27

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, DOI: https://doi.org/10.1515/anly-2012-1236.

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