Yazar "Yilmaz, Basar" seçeneğine göre listele

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    A Class of Integral Operators that Fix Exponential Functions
    (Springer Basel Ag, 2021) Bardaro, Carlo; Mantellini, Ilaria; Uysal, Gumrah; Yilmaz, Basar
    In this paper we introduce a general class of integral operators that fix exponential functions, containing several recent modified operators of Gauss-Weierstrass, or Picard or moment type operators. Pointwise convergence theorems are studied, using a Korovkin-type theorem and a Voronovskaja-type formula is obtained.
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    A NOTE ON KANTOROVICH TYPE BERNSTEIN CHLODOVSKY OPERATORS WHICH PRESERVE EXPONENTIAL FUNCTION
    (Element, 2021) Aral, Ali; Ari, Didem Aydin; Yilmaz, Basar
    This paper is mainly focused on the integral extension of Bernstein-Chlodovsky operators which preserve exponential function. Inspire of the Bernstein-Chlodovsky operators which preserve exponential function, we define the integral extension of these operators by using a different technique. We give weighted approximation properties including a weighted uniform convergence and a weighted quantitative theorem in terms of exponential weighted modulus of continuity. Furthermore, we give the Voronovskaya type theorem.
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    APPROXIMATION PROPERTIES OF MODIFIED GAUSS-WEIERSTRASS INTEGRAL OPERATORS IN EXPONENTIAL WEIGHTED Lp SPACES
    (Univ Nis, 2021) Yilmaz, Basar
    In this paper, we deal with modified Gauss-Weierstrass integral operators from exponentially weighted spaces L-p,L-a (R) into L-p,L-2a (R). We give the rate of convergence in terms of weighted modulus of continuity. Moreover, we prove weighted approximation of functions belonging to the space L-p,L-a (R) by these operators with the help of a Korovkin type theorem. Finally, we give pointwise approximation of such functions by these operators at generalized Lebesgue points.
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    Jackson Type Generalization of Nonlinear Integral Operators
    (Eudoxus Press, Llc, 2014) Yilmaz, Basar
    In this work, we provides a global smoothness preservation result of a Jackson-type generalization of the nonlinear convolution operator defined by Angeloni and Vinti in [4]. Convergence in variation is also studied.
  • Küçük Resim
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    A note on the modified Picard integral operators
    (WILEY, 2020) Yilmaz, Basar; Aydin Ari, Didem
    This study is a natural continuation of modified Picard operators, defined by Agratini et al, preserving an exponential function. Herein, we first show that these operators are approximation processes in the setting of large classes of weighted spaces. Then, we obtain weighted uniform convergence of the operators via exponential weighted modulus of smoothness. Finally, we give, by using the weighted modulus of continuity, the result regarding global smoothness preservation properties for the generalized Picard operators, which based in Agratini et al.
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    Quantitative type theorems in the space of locally integrable functions
    (Springer, 2022) Aral, Ali; Ozsarac, Firat; Yilmaz, Basar
    In this work, we introduce a new modulus of continuity for locally integrable function spaces which is influenced by the natural structure of the L-p space. After basic properties of it are given, we obtain a quantitative type theorem for the rate of convergence of convolution type integral operators and iterates of them. Their global smoothness preservation property involving the new modulus of continuity is presented. Finally, the obtained results are applied to Gauss-Weierstrass operators.
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    RECONSTRUCTION OF TWO APPROXIMATION PROCESSES IN ORDER TO REPRODUCE eax AND e2ax, a > 0
    (Element, 2021) Yilmaz, Basar; Uysal, Gumrah; Aral, Ali
    We propose two modifications for Gauss-Weierstrass operators and moment-type operators which fix e(ax) and e(2ax) with a> 0. First, we present moment identities for new operators. Then, we discuss weighted approximation and prove Voronovskaya-type theorems for them in exponentially weighted spaces. Using modulus of continuity in exponentially weighted spaces, we obtain some global smoothness preservation properties. We give a comparison result for Gauss-Weierstrass operators. Finally, we provide some graphical illustrations that show that modified operators perform better than classical ones.
  • Küçük Resim
    Öğe
    Weighted approximation by modified Picard operators
    (SPRINGER, 2020) Aral, Ali; Yilmaz, Basar; Deniz, Emre
    Herein, the aim is to further investigate the properties of the generalized Picard operators introduced in Agratini et al. (Positivity 3(21):1189-1199, 2017). The motivation is based on with the purpose of furnishing appropriate positive approximation processes in the setting of large classes of exponential weighted Lp spaces via different type theorems. For this propose, firstly we give the boundness of the operators, acting from an exponential weighted space into itself. Also, using an exponential weighted modulus of continuity a quantitative type theorem as well as the global smoothness property of the operators are presented. Then, we give pointwise approximation property of the operators at a generalized Lebesgue point. Finally under a certain condition, again the weighted Lp approximation is formulated without using Korovkin type theorem.