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http://yadda.icm.edu.pl:80/baztech/element/bwmeta1.element.baztech-670c89df-3e96-49fb-9e0d-1de33a9de6c1

Czasopismo

Demonstratio Mathematica

Tytuł artykułu

Some convergence results for nonlinear singular integral operators

Autorzy Karsli, H. 
Treść / Zawartość https://www.degruyter.com/view/j/dema
Warianty tytułu
Języki publikacji EN
Abstrakty
EN In this paper, we establish some pointwise convergence results for a family of certain nonlinear singular integral operators Tλf of the form (...), acting on functions with bounded (Jordan) variation on an interval [a, b] as λ→λ0. Here, the kernels (...) satisfy some suitable singularity assumptions. We remark that the present study is a continuation and extension of the study of pointwise approximation of the family of nonlinear singular integral operators (1) begun in [18].
Słowa kluczowe
PL zmienność ograniczona   warunek Lipschitza   zbieżność punktowa  
EN nonlinear singular integrals   bounded variation   Lipschitz condition   pointwise convergence  
Wydawca De Gruyter
Czasopismo Demonstratio Mathematica
Rocznik 2013
Tom Vol. 46, nr 4
Strony 729--740
Opis fizyczny Bibliogr. 23 poz.
Twórcy
autor Karsli, H.
  • Abant Izzet Baysal University, Faculty of Science and Arts, Department of Mathematics, 14280 Golkoy Bolu, karsli_h@ibu.edu.tr
Bibliografia
[1] L. Angeloni, G. Vinti, Convergence in variation and rate of approximation for nonlinear integral operators of convolution type, Results Math. 49 (2006), 1–23. Erratum: 57 (2010), 387–391.
[2] L. Angeloni, G. Vinti, Approximation by means of nonlinear integral operators in the space of functions with bounded -variation, Differential Integral Equations 20 (2007), 339–360. Erratum: 23(7–8) (2010), 795–799.
[3] L. Angeloni, G. Vinti, Convergence and rate of approximation for linear integral operators in BV-spaces in multidimensional setting, J. Math. Anal. Appl. 349 (2009), 317–334.
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[6] C. Bardaro, H. Karsli, G. Vinti, On pointwise convergence of linear integral operators with homogeneous kernels, Integral Transforms Spec. Funct. 19(6) (2008), 429–439.
[7] C. Bardaro, H. Karsli, G. Vinti, Nonlinear integral operators with homogeneous kernels: pointwise approximation theorems, Appl. Anal. 90(3,4) (2011), 463–474.
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[12] P. L. Butzer, R. J. Nessel, Fourier Analysis and Approximation, Vol. 1, Academic Press, New York, London, 1971.
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[15] Y. H. Hua, S. Y. Shaw, Rate of approximation for functions of bounded variation by integral operators, Period. Math. Hungar. 46(1) (2003), 41–60.
[16] H. Karsli, Convergence and rate of convergence by nonlinear singular integral operators depending on two parameters, Appl. Anal. 85(6,7) (2006), 781–791.
[17] H. Karsli, On approximation properties of a class of convolution type nonlinear singular integral operators, Georgian Math. J. 15(1) (2008), 77–86.
[18] H. Karsli, V. Gupta, Rate of convergence by nonlinear integral operators for functions of bounded variation, Calcolo 45(2) (2008), 87–99.
[19] H. Karsli, E. Ibikli, On convergence of convolution type singular integral operators depending on two parameters, Fasc. Math. 38 (2007), 25–39.
[20] J. Musielak, On some approximation problems in modular spaces, in: Constructive Function Theory, 1981, Proc. Int. Conf., Varna, June 1–5, 1981, pp. 455–461, Publ. House Bulgarian Acad. Sci., Sofia, 1983.
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[23] X. M. Zeng, W. Chen, On the rate of convergence of the generalized Durrmeyer type operators for functions of bounded variation, J. Approx. Theory 102 (2000), 1–12
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