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    A-statistical relative modular convergence of positive linear operators
    (Springer, 2017) Demirci, Kamil; Kolay, Burcak
    In this paper, we investigate the problem of statistical approximation to a function f by means of positive linear operators defined on a modular space. Particularly, in order to get stronger results than the classical aspects we mainly use the concept of statistical convergence. Also, a non-trivial application is presented.
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    Öğe
    Korovkin type approximation for double sequences via statistical A-summation process on modular spaces
    (Univ Babes-Bolyai, 2018) Orhan, Sevda; Kolay, Burcak
    In this work, we introduce the Korovkin type approximation theorems on modular spaces via statistical A-summation process for double sequences of positive linear operators and we construct an example satisfying our new approximation theorem but does not satisfy the classical one.
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    Öğe
    Statistical relative A-summation process for double sequences on modular spaces
    (Springer-Verlag Italia Srl, 2018) Demirci, Kamil; Orhan, Sevda; Kolay, Burcak
    In the present paper, we extend the Korovkin type approximation theorem via statistical relative A- summation process onto the double sequences of positive linear operators in a modular space. Then we discuss the reduced results which are obtained by special choice of the scale function and the matrix sequences. We apply our new result to bivariate Bernstein- Kantorovich operators in Orlicz spaces and hence we show that it is stronger than the results obtained previously.
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    Öğe
    Statistical Relative Α-Summation Process and Korovkin-Type Approximation Theorem on Modular Spaces
    (Springer International Publishing Ag, 2018) Kolay, Burcak; Orhan, Sevda; Demirci, Kamil
    In this paper, we present the notion of relative Alpha-summation process. Then we give a statistical Korovkin-type approximation theorem via relative Alpha-summation process in the setting of modular spaces, which includes as particular cases Lp, Orlicz and Musielak-Orlicz spaces. Finally, we give an example showing that our results are proper extensions of the corresponding ones.