Browsing by Author "Bayram, Nilay Sahin"

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    Approximation by statistical convergence with respect to power series methods
    (2022) Bayram, Nilay Sahin; Yildiz, Sevda
    In the present work, using statistical convergence with respect to power series methods, we obtain various Korovkin-type approximation theorems for linear operators defined on derivatives of functions. Then we give an example satisfying our approximation theorem. We study certain rate of convergence related to this method. In the final section we summarize these results to emphasize the importance of the study.
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    An extension of Korovkin theorem via power series method
    (2022) Yildiz, Sevda; Bayram, Nilay Sahin
    In the present work, using the power series method, we obtain various Korovkin-type approximation theorems for linear operators defined on derivatives of functions. We also explain that our theorem makes more sense with a striking example. We study the quantitative estimates of linear operators. In the final section, we summarize our new results.
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    Power Series Methods And Statistical Limit Superior
    (2022) Bayram, Nilay Sahin
    Given a real bounded sequence x = (xj) and an infinite matrix A = (anj) the Knopp core theorem is equivalent to study the inequality lim sup Ax <= lim sup x. Recently Fridy and Orhan [6] have considered some variants of this inequality by replacing lim sup x with statistical limit superior st - lim sup x. In the present paper we examine similar type of inequalities by employing a power series method P, a non-matrix sequence-to-function trans-formation, in place of A = (anj) .
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    A - Summation process in the space of locally integrable functions
    (2020) Bayram, Nilay Sahin; Orhan, Cihan
    In this paper, using the concept of summation process, we give a Korovkin type approximation theorem for a sequence of positive linear operators acting from L-p,L-q (loc), the space of locally integrable functions, into itself. We also study rate of convergence of these operators.