Yazar "Duman, Oktay" seçeneğine göre listele

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    Öğe
    APPROXIMATION IN STATISTICAL SENSE TO B-CONTINUOUS FUNCTIONS BY POSITIVE LINEAR OPERATORS
    (Akademiai Kiado Rt, 2010) Dirik, Fadime; Duman, Oktay; Demirci, Kamil
    In the present work, using the concept of A-statistical convergence for double real sequences, we obtain a statistical 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. Furthermore, we display an application which shows that our new result is stronger than its classical version.
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    Öğe
    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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    Öğe
    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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    Öğe
    Statistical approximation to Bogel-type continuous and periodic functions
    (De Gruyter Poland Sp Zoo, 2009) Dirik, Fadime; Duman, Oktay; Demirci, Kamil
    In this paper, considering A-statistical convergence instead of Pringsheim's sense for double sequences, we prove a Korovkin-type approximation theorem for sequences of positive linear operators defined on the space of all real valued Bogel-type continuous and periodic functions on the whole real two-dimensional space. A strong application is also presented. Furthermore, we obtain some rates of A-statistical convergence in our approximation.