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    On Some Spaces Isomorphic to the Space of Absolutely q-summable Double Sequences
    (Kyungpook Natl Univ, Dept Mathematics, 2018) Capan, Husamettin; Basar, Feyzi
    Let 0 < q < infinity. In this study, we introduce the spaces BVq and LSq of q-bounded variation double sequences and q-summable double series as the domain of four-dimensional backward difference matrix Delta and summation matrix S in the space L-q of absolutely q-summable double sequences, respectively. Also, we determine their alpha- and beta-duals and give the characterizations of some classes of four-dimensional matrix transformations in the case 0 < q <= 1.
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    On the difference spaces of almost convergent and strongly almost convergent double sequences
    (Springer, 2019) Capan, Husamettin; Basar, Feyzi
    In this paper, we study the difference spaces F(), F0(), [F]() and [F]0() of double sequences obtained as the domain of four-dimensional backward difference matrix in the spaces F, F0, [F] and [F]0 of almost convergent, almost null, strongly almost convergent and strongly almost null double sequences; respectively. We examine general topological properties of those spaces and give some inclusion theorems. Furthermore, we deal with their dual spaces.
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    On the Paranormed Space L(t) of Double Sequences
    (Univ Nis, Fac Sci Math, 2018) Capan, Husamettin; Basar, Feyzi
    In this paper, we introduce the paranormed sequence space L(t) which is the generalization of the space L q of all absolutely q summable double sequences. We examine some topological properties of the space L(t) and determine its alpha-, beta -and gamma-duals. Finally, we characterize some classes of four-dimensional matrix transformations from the space L(t) into some spaces of double sequences.