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    AK(V)-Property of Double Series Spaces
    (Springernature, 2021) Yesilkayagil, Medine; Basar, Feyzi
    In the present paper, we show that V-convergent double series spaces CSV and the series space BV of double sequences of bounded variation are BDK-spaces and investigate their AK (V)-space property, where V is an element of {p, bp, r}.
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    Domain of Riesz mean in some spaces of double sequences
    (Elsevier Science Bv, 2018) Yesilkayagil, Medine; Basar, Feyzi
    In this study, we define the double sequence spaces (M-u)(Rqt), (Cp)(Rqt), (C-bp)(Rqt) and (C-r)(Rqt) as the domain of four dimensional Riesz mean R-qt in the spaces M-u, C-p, C-bp and C-r, respectively. Then, we examine some topological properties of those sequence spaces and we characterize the RH-regularity of the Riesz mean R-qt. Taking v is an element of{p, bp, r}, we determine the beta(v)-duals of the spaces (C-v)(Rqt) and we characterize the classes ((C-r)(Rqt) : C-v), (mu : (C-v)(Rqt)) and ((C-v)(Rqt) : C-f) of four-dimensional matrix transformations, where mu and C-f denote any given double sequence space and the space of almost convergent double sequences, respectively. (C) 2018 Published by Elsevier B.V. on behalf of Royal Dutch Mathematical Society (KWG).
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    A NOTE ON SOME TOPOLOGICAL PROPERTIES OF KOTHE SPACE ?(P)
    (Publications L Institut Mathematique Matematicki, 2019) Yesilkayagil, Medine; Basar, Feyzi
    We emphasize some topological properties of the Kothe space lambda(P) determined by a Kothe set P.
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    On the Paranormed Space of Bounded Variation Double Sequences
    (Springernature, 2020) Yesilkayagil, Medine; Basar, Feyzi
    In this study, as the domain of four-dimensional backward difference matrix in the space Lu(t), we introduce the complete paranormed space BV(t) of bounded variation double sequences and examine some properties of that space. Also, we determine the gamma-dual and beta(theta)-dual of the space BV(t). Finally, we characterize the classes (BV(t):Mu), (BV(t):C theta) and (Lu(t):mu) with mu is an element of{BS,CS theta,Mu(Delta),C theta(Delta)}, where Mu(Delta) and C theta(Delta) denote the spaces of all double sequences whose Delta-transforms are in the spaces Mu and C theta, respectively.
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    A Study on Certain Kothe Spaces
    (Univ Nis, Fac Sci Math, 2018) Yesilkayagil, Medine; Basar, Feyzi
    Let A = (a(nk)) be a Kothe matrix. In this paper, we introduce the space lambda(bs)(A) and we emphasize on some topological properties of the spaces c(0)(A), lambda(bs)(A) and lambda(p)(A) together with some inclusion relations, where 1 <= p <= infinity.
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    A SURVEY FOR PARANORMED SEQUENCE SPACES GENERATED BY INFINITE MATRICES
    (Inst Applied Mathematics, 2019) Basar, Feyzi; Yesilkayagil, Medine
    In the present paper, we summarize the recent literature concerning the domains of triangles in Maddox's sequence spaces l(infinity)(p), c(p), c(0)(p) and l(p), and related topics.
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    A Survey for the Spectrum of Triangles over Sequence Spaces
    (Taylor & Francis Inc, 2019) Yesilkayagil, Medine; Basar, Feyzi
    In the present paper, we summarize the recent literature concerning the spectrum and fine spectrum with respect to Goldberg's classification of some operators represented by an infinite matrix over certain sequence spaces.