Yazar "Cinar, Selin" seçeneğine göre listele

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    Approximation of matrix-valued functions via statistical convergence with respect to power series methods
    (Springernature, 2022) Demirci, Kamil; Yildiz, Sevda; Cinar, Selin
    In this paper, we deal with an approximation problem for matrix-valued positive linear operators via statistical convergence with respect to the power series method which is a new statistical type convergence. Then, we present an application that shows our theorem is more applicable than the classical one. We also compute the rates of P-statistical convergence of these operators.
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    Korovkin type approximation via triangular A-statistical convergence on an infinite interval
    (Tubitak Scientific & Technological Research Council Turkey, 2021) Cinar, Selin; Yildiz, Sevda; Demirci, Kamil
    In the present paper, using the triangular A-statistical convergence for double sequences, which is an interesting convergence method, we prove a Korovkin-type approximation theorem for positive linear operators on the space of all real-valued continuous functions on [0, infinity) x [0, infinity) with the property that have a finite limit at the infinity. Moreover, we present the rate of convergence via modulus of continuity. Finally, we give some further developments.
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    P-statistical summation process of sequences of convolution operators
    (Indian Nat Sci Acad, 2022) Cinar, Selin; Yildiz, Sevda
    In the present paper, we make a study of P-statistical Korovkin theorem via A-summation process for a sequence of positive linear convolution operators and we show that our results obtained via an interesting application are meaningful. We also analyze rate of convergence of these operators via modulus of continuity.
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    Statistical convergence with respect to power series method on product time scales
    (Univ Nis, Fac Sci Math, 2024) Demirci, Kamil; Cinar, Selin; Yildiz, Sevda
    In this paper, we will give some new notions on arbitrary product time scales using statistical convergence in the sense of the power series method. We will then use these new concepts to present developments in the literature.
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    TRIANGULAR A-STATISTICAL RELATIVE UNIFORM CONVERGENCE FOR DOUBLE SEQUENCES OF POSITIVE LINEAR OPERATORS
    (Univ Nis, 2021) Cinar, Selin
    In this paper, we introduce the concept of triangular A-statistical relative convergence for double sequences of functions defined on a compact subset of the real two-dimensional space. Based upon this new convergence method, we prove Korovkin-type approximation theorem. Finally, we give some further developments.
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    Triangular ideal relative convergence on modular spaces and Korovkin theorems
    (Univ Babes-Bolyai, 2023) Cinar, Selin; Yildiz, Sevda
    In this paper, we introduce the concept of triangular ideal relative convergence for double sequences of functions defined on a modular space. Based upon this new convergence method, we prove Korovkin theorems. Then, we construct an example such that our new approximation results work. Finally, we discuss the reduced results which are obtained by special choices.