Yazar "Karabiyik, Umit" seçeneğine göre listele

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    Almost Sequence Spaces Derived by the Domain of the Matrix Ar
    (Hindawi Ltd, 2013) Karaisa, Ali; Karabiyik, Umit
    By using A(r), we introduce the sequence spaces a(f)(r), a(f0)(r), and a(fs)(r) of normed space and BK-space and prove that a(f)(r), a(f0)(r), and a(fs)(r) are linearly isomorphic to the sequence spaces f, f(0), and fs, respectively. Further, we give some inclusion relations concerning the spaces a(f)(r), a(f0)(r) and the nonexistence of Schauder basis of the spaces fs and a(fs)(r) is shown. Finally, we determine the beta- and gamma-duals of the spaces a(f)(r) and a(fs)(r). Furthermore, the characterization of certain matrix classes on new almost convergent sequence and series spaces has exhaustively been examined.
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    On Some Properties Paranormed Sequence Spaces Generated by Generalized Sequence Means and Core Theorems
    (Chiang Mai Univ, Fac Science, 2017) Karaisa, Ali; Karabiyik, Umit
    Recently, Mursaleen and Noman constructed new sequence spaces by using a matrix domain over a normed space [On generalized means and some related sequence spaces, Comput. Math. Appl. 61 (2011) 988-999]. They also studied some topological properties of these spaces. In this work, we generalize the normed sequence space defined by Mursaleen and Noman to paranormed space. Furthermore, we introduce new sequence space over the paranormed space by using the expansion method. Then, we investigate some topological properties. Finally, we introduce generalized means core of a complex-valued sequence prove some inclusion theorems related to this new type of core.