Yazar "Karakus, Sevda" seçeneğine göre listele

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    A-summation process and Korovkin-type approximation theorem for double sequences of positive linear operators
    (Walter De Gruyter Gmbh, 2012) Karakus, Sevda; Demirci, Kamil
    The aim of this paper is to present a Korovkin-type approximation theorem on the space of all continuous real valued functions on any compact subset of the real two-dimensional space by using a A-summation process. We also study the rates of convergence of positive linear operators with the help of the modulus of continuity.
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    Equi-statistical convergence of positive linear operators
    (Academic Press Inc Elsevier Science, 2008) Karakus, Sevda; Demirci, Kamil; Duman, Oktay
    Balcerzak, Dems and Komisarski [M. Balcerzak, K. Dems, A. Komisarski, Statistical convergence and ideal convergence for sequences of functions, J. Math. Anal. Appl. 328 (2007) 715-729] have recently introduced the notion of equi-statistical convergence which is stronger than the statistical uniform convergence. In this paper we study its use in the Korovkin-type approximation theory. Then, we construct an example such that our new approximation result works but its classical and statistical cases do not work. We also compute the rates of equi-statistical convergence of sequences of positive linear operators. Furthermore, we obtain a Voronovskaya-type theorem in the equi-statistical sense for a sequence of positive linear Operators constructed by means of the Bernstein polynomials. (C) 2007 Elsevier Inc. All rights reserved.
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    Equi-statistical σ-convergence of positive linear operators
    (Pergamon-Elsevier Science Ltd, 2010) Karakus, Sevda; Demirci, Kamil
    In this paper we introduce the notion of equi-statistical a-convergence which is stronger than the uniform convergence (in the ordinary sense), statistical uniform convergence and statistical uniform a-convergence. Then, we also give its use in the Korovkin-type approximation theory. We also compute the rate of equi-statistical sigma-convergence of a sequence of positive linear operators. (C) 2010 Elsevier Ltd. All rights reserved.
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    Korovkin-Type Approximation Theorem for Double Sequences of Positive Linear Operators via Statistical A-Summability
    (Springer Basel Ag, 2013) Demirci, Kamil; Karakus, Sevda
    In this paper, using the concept of statistical A-summability which is stronger than the A-statistical convergence we provide a Korovkin-type approximation theorem on the space of all continuous real valued functions defined on any compact subset of the real two-dimensional space. We also study the rates of statistical A-summability of positive linear operators.
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    Statistical A-summability of positive linear operators
    (Pergamon-Elsevier Science Ltd, 2011) Demirci, Kamil; Karakus, Sevda
    In this paper, using the concept of statistical A-summability which is stronger than the A-statistical convergence we provide a Korovkin-type approximation theorem. We also compute the rates of statistical A-summability of a sequence of positive linear operators. (C) 2010 Elsevier Ltd. All rights reserved.
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    Statistical approximation by positive linear operators on modular spaces
    (Springer, 2010) Karakus, Sevda; Demirci, Kamil; Duman, Oktay
    In this paper, we investigate the problem of statistical approximation to a function by means of positive linear operators defined on a modular space. Especially, in order to get more powerful results than the classical aspects we mainly use the concept of statistical convergence. A non-trivial application is also presented.
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    STATISTICAL σ APPROXIMATION TO BOGEL-TYPE CONTINUOUS FUNCTIONS
    (Akademiai Kiado Zrt, 2011) Karakus, Sevda; Demirci, Kamil
    In this paper, using the concept of statistical a-convergence which is stronger than the statistical convergence, we obtain a statistical a-approximation theorem for sequences of positive linear operators defined on the space of all real valued B-continuous functions on a compact subset of the real line. Then, we construct an example such that our new approximation result works but its classical and statistical cases do not work. Also we compute the rate of statistical a-convergence of sequence of positive linear operators.
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    Statistical σ approximation to max-product operators
    (Pergamon-Elsevier Science Ltd, 2011) Karakus, Sevda; Demirci, Kamil
    In this paper, using the concept of statistical sigma-convergence which is stronger than statistical convergence, we obtain a statistical sigma approximation theorem for a general sequence of max-product operators, including Shepard type operators, although its classical limit fails. We also compute the corresponding statistical sigma rates of the approximation. (C) 2010 Elsevier Ltd. All rights reserved.