Almost convergence and generalized difference matrix

Let f denotes the space of almost convergent sequences introduced by Lorentz [G.G. Lorentz, A contribution to the theory of divergent sequences, Acta Math. 80 (1948), 167–190] and f ̂ also be the domain of the generalized difference matrix B ( r , s ) in the sequence space f . In this paper, the β -...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2011-02, Vol.61 (3), p.602-611
Main Authors: Basar, Feyzi, Kirisci, Murat
Format: Article
Language:English
Subjects:
[formula omitted]- and [formula omitted]-duals and matrix transformations
Almost convergence
Convergence
Mathematical analysis
Mathematical models
Matrices
Matrix domain of a sequence space
Matrix methods
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Summary:Let f denotes the space of almost convergent sequences introduced by Lorentz [G.G. Lorentz, A contribution to the theory of divergent sequences, Acta Math. 80 (1948), 167–190] and f ̂ also be the domain of the generalized difference matrix B ( r , s ) in the sequence space f . In this paper, the β - and γ -duals of the spaces f , f s and f ̂ are determined. Furthermore, two basic results on the space f are proved and the classes ( f ̂ : μ ) and ( μ : f ̂ ) of infinite matrices are characterized, and the characterizations of some other classes are also given as an application of those main results, where μ is any given sequence space.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2010.12.006