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    Öğe
    Multiplier Sequence Spaces Defined by Statistical Summability and Orlicz-Pettis Theorem
    (Taylor & Francis Inc, 2021) Kama, Ramazan; Altay, Bilal
    In this paper, we introduce some new multiplier spaces related to a series Sigma(i)x(i) in a normed space X through f-statistical summability and give some characterizations of completeness and barrelledness of the spaces through weakly unconditionally Cauchy series in X and X*, respectively. We also obtain a new version of the Orlicz-Pettis theorem within the frame of the f-statistical convergence.
  • Küçük Resim
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    On Cesàro summability of vector valued multiplier spaces and operator valued series
    (2018) Altay, Bilal; Kama, Ramazan
    In this paper, we introduce and study vector valued multiplier spaces with the help of the sequence of continuous linear operators between normed spaces and Cesàro convergence. Also, we obtain a new version of the Orlicz–Pettis Theorem by means of Cesàro summability.
  • [ X ]
    Öğe
    On f-strongly Cesaro and f-statistical derivable functions
    (Amer Inst Mathematical Sciences-Aims, 2022) Altay, Bilal; Garcia-Pacheco, Francisco Javier; Kama, Ramazan
    In this manuscript, we introduce the following novel concepts for real functions related to f-convergence and f-statistical convergence: f-statistical continuity, f-statistical derivative, and f-strongly Cesaro derivative. In the first subsection of original results, the f-statistical continuity is related to continuity. In the second subsection, the f-statistical derivative is related to the derivative. In the third and final subsection of results, the f-strongly Cesaro derivative is related to the strongly Cesaro derivative and to the f-statistical derivative. Under suitable conditions of the modulus f, several characterizations involving the previous concepts have been obtained.
  • Küçük Resim
    Öğe
    Weakly unconditionally Cauchy series and Fibonacci sequence spaces
    (Springer International Publishing, 2017) Kama, Ramazan; Altay, Bilal
    We study new sequence spaces associated to sequences in normed spaces and the band matrix F̂ defined by the Fibonacci sequence. We give some characterizations of continuous linear operators and weakly unconditionally Cauchy series by means of completeness of the new sequence spaces. Also, we characterize the barreledness of a normed space via weakly∗ unconditionally Cauchy series in X*.