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Singular integral equations with multiplicative Cauchy-type kernels

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Języki publikacji
EN
Abstrakty
EN
In this paper we consider singular integral equations of the first kind with multiplicative Cauchy-type kernels defined on n-dimensional domains. We give their general solutions in the class of Holder continuous functions and propose the statements of uniqueness problem.
Rocznik
Tom
Strony
77--90
Opis fizyczny
Bibliog. 29 poz.
Twórcy
autor
  • Institute of Mathematics and Computer Science The John Paul II Catholic University of Lublin Al. Racławickie 14, 20-950 Lublin, Poland Department of Electrical and Computer Engineering University of Alberta 9107 - 116 Street, Edmonton, AB, Canada T6G 2V4
autor
  • Institute of Mathematics and Computer Science The John Paul II Catholic University of Lublin Al. Racławickie 14, 20-950 Lublin, Poland
autor
  • Institute of Mathematics and Computer Science The John Paul II Catholic University of Lublin Al. Racławickie 14, 20-950 Lublin, Poland
Bibliografia
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  • [3] Akel M.S., Hussein H.S., Numerical treatment of solving singular integral equations by using Sinc approximations, Appl. Math. Comput., 218(2011), 3565-3573.
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  • [7] Chen Z., Wang C., Zhou Y., A new method for solving Cauchy type singular integral equations of the second kind, Int. J. Comput. Math., 87(2010), 2076-2087.
  • [8] Ditkin V.A., Prudnikov A.P., Integral Transforms and Operational Calculus, Pergamon Press, New York, 1965.
  • [9] Dzhuraev A., Methods of Singular Integral Equations, Longman Scientific & Technical, Harlow, 1992.
  • [10] Erdogan F., Gupta G.D., Cook T.S., Numerical solution of singular integral equations, in: Mechanics of Fracture, 1, 368—425, Noordhoff International Publishing, Leiden, 1973.
  • [11] Estrada R., Kanwal R.P., Singular Integral Equations, Birkhauser, Boston, 2000.
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  • [14] Karczmarek P., Singular integral equation with a multiplicative Cauchy kernel in the half-plane, Opuscula Math., 28(2008), 63-72.
  • [15] Karczmarek P., Application of Chebyshev and trigonometric polynomials to the approximation of a solution of a singular integral equation with a multiplicative Cauchy kernel in the half-plane, Opuscula Math., 28(2008), 129-136.
  • [16] Karczmarek P., Approximate solution of a singular integral equation with a multiplicative Cauchy kernel in the half-plane, Comput. Methods Appl. Math., 8(2008), 143-154.
  • [17] Karczmarek P., Numerical Solution of Singular Integral Equation in the Half-Plane, in: L. Gadomski, M. Jakubiak, A. N. Prokopenya (eds.), Computer Algebra Systems in Teaching and Research. Differential Equations, Dy¬namical Systems and Celestial Mechanics, Collegium Mazovia, Siedlce, 2011, 46-57.
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  • [19] Lifanow I.K., Poltavskii L.N., Vainikko G.M., Hypersigular Integral Equations and Their Applications, Chapman & Hall/CRC, Boca Raton, 2004.
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Bibliografia
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