On the difference spaces of almost convergent and strongly almost convergent double sequences

Çapan, Hüsamettin; Başar, Feyzı

doi:10.1007/s11117-018-0620-3

Cited by 6 publications

(3 citation statements)

References 19 publications

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“…The matrix domain on some almost convergent single sequence spaces have been done by several mathematicians (see [31,32,33,34]). The idea of calculating four-dimensional matrix domain on almost convergent double sequences spaces is a new subject and studied by a few mathematicians (see [3,4,19]).…”

Section: Resultsmentioning

confidence: 99%

“…In this paper, as a natural continuation of the papers [3,4,19] we calculated the four-dimensional generalized difference matrix B…”

Section: Resultsmentioning

confidence: 99%

“…In this paper, as a natural continuation of the papers [3,4,19] we calculated the four-dimensional generalized difference matrix B(r, s, t, u) domain Similar works can be done by letting other four-dimensional matrices domain on almost convergent double sequences and new matrix classes including [C f ] can be characterized for the further studies.…”

Section: Discussionmentioning

confidence: 99%

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Four-Dimensional Generalized Difference Matrix and Almost Convergent Double Sequence Spaces

Tuǧ

2017

Springer Proceedings in Mathematics &Amp; Statistics

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Most recently, some new double sequence spaces B(Mu), B(C ϑ ) where ϑ = {b, bp, r, f, f 0 } and B(Lq) for 0 < q < ∞ have been introduced as four-dimensional generalized difference matrix B(r, s, t, u) domain on the double sequence spaces Mu, C ϑ where ϑ = {b, bp, r, f, f 0 } and Lq for 0 < q < ∞, and some topological properties, dual spaces, some new four-dimensional matrix classes and matrix transformations related to these spaces have also been studied by Tuğ and Başar and Tuğ (see [1,2,3,4]). In this present paper, we introduce new strongly almost null and strongly almost convergent double sequence spaces B[C f ] and B[C f 0 ] as domain of four-dimensional generalized difference matrix B(r, s, t, u) in the spaces [C f ] and [C f 0 ], respectively. Firstly, we prove that the new double sequence spaces B[C f ] and B[C f 0 ] are Banach spaces with its norm. Then, we give some inclusion relations including newly defined strongly almost convergent double sequence spaces. Moreover, we calculate the α−dual, β(bp)−dual and γ−dual of the space B[C f ]. Finally, we characterize new four-dimensional matrix classes ([C f ]; C f ), ([C f ]; Mu), (B[C f ]; C f ), (B[C f ]; Mu) and we complete this work with some significant results. 2010 Mathematics Subject Classification. 46A45, 40C05.

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