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A method for solving general singular equations and its application

Year 2019, Volume: 68 Issue: 1, 871 - 882, 01.02.2019
https://doi.org/10.31801/cfsuasmas.484955

Abstract

In this paper we present a new method for solving general singular equations of normal type. As an application of this method, we give a solution for a class of convolution-type integral equations

References

  • Atkinson, F.V., The normal solubility of linear equations in normed spaces, Mat. Sbornik N.S. 28(70) (1951), 3--14. (in Russian)
  • Cherskii, Yu.I., The general singular equation and equations of convolution type, Mat.Sb.N.S., 41(83):3 (1957), 277--296. (in Russian)
  • Gakhov, F.D., Boundary Value Problems, Pergamon Press, Oxford-New York-Paris; Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1966.
  • Gakhov F. D. and Cherskii, Yu. I., Singular integral equations of convolution type, Izv. Akad. Nauk SSSR. Ser.Mat. 20 (1956), 33--52. (in Russian)
  • Halmos, P.R., A Hilbert Space Problem Book, Springer-Verlag, Berlin-New York, 1978.
  • Helemskii, A.Y., Lectures and Exercises on Functional Analysis, Moscow State University; AMS, Vol.233, 2006.
  • Khalilov, Z. I., Linear singular equations in a normed ring, Izvestiya Akad. Nauk SSSR. Ser. Mat. 13 (1949), 163--176. (in Russian)
  • Khvedelidze, B.V., Linear discontinuous boundary problems in the theory of functions, singular integral equations and some applications, Trudy Tbilis. Mat. Inst. Akad. Nauk. GruzSSR , 23 (1956) pp. 3--158 (In Russian) \bibitem[Mi]{mik} S.G. Mikhlin, Singular integral equations, \emph{Uspekhi Mat. Nauk}, 3:3(25) (1948), 29--112. (Russian)
  • Muskhelishvili, N.I., Singular integral equations. Boundary problems of function theory and their application to mathematical physics, Noordhoff International Publishing, Leyden, 1977.
  • Przeworska-Rolewicz, D. and Rolewicz, S., Equations in general spaces, Polish Scientific Publishers, Warsaw, 1968.
  • Simonenko, I.B., Riemann's boundary value problem with a continuous coefficient, Dokl. Akad. Nauk SSSR 124 (1959), 278--281. (in Russian)
  • Titchmarsh, E.C., Introduction to the Theory of Fourier Integrals, The Clarendon Press, Oxford University Press, New York, 1937.
  • Vekua, N.P., Systems of singular integral equations and some boundary value problems, Moscow (1970) (in Russian)
  • Yosida, K., Functional analysis Fourth edition. Die Grundlehren der mathematischen Wissenschaften, Band 123. Springer-Verlag, New York-Heidelberg, xii+496 pp. 1974.
Year 2019, Volume: 68 Issue: 1, 871 - 882, 01.02.2019
https://doi.org/10.31801/cfsuasmas.484955

Abstract

References

  • Atkinson, F.V., The normal solubility of linear equations in normed spaces, Mat. Sbornik N.S. 28(70) (1951), 3--14. (in Russian)
  • Cherskii, Yu.I., The general singular equation and equations of convolution type, Mat.Sb.N.S., 41(83):3 (1957), 277--296. (in Russian)
  • Gakhov, F.D., Boundary Value Problems, Pergamon Press, Oxford-New York-Paris; Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1966.
  • Gakhov F. D. and Cherskii, Yu. I., Singular integral equations of convolution type, Izv. Akad. Nauk SSSR. Ser.Mat. 20 (1956), 33--52. (in Russian)
  • Halmos, P.R., A Hilbert Space Problem Book, Springer-Verlag, Berlin-New York, 1978.
  • Helemskii, A.Y., Lectures and Exercises on Functional Analysis, Moscow State University; AMS, Vol.233, 2006.
  • Khalilov, Z. I., Linear singular equations in a normed ring, Izvestiya Akad. Nauk SSSR. Ser. Mat. 13 (1949), 163--176. (in Russian)
  • Khvedelidze, B.V., Linear discontinuous boundary problems in the theory of functions, singular integral equations and some applications, Trudy Tbilis. Mat. Inst. Akad. Nauk. GruzSSR , 23 (1956) pp. 3--158 (In Russian) \bibitem[Mi]{mik} S.G. Mikhlin, Singular integral equations, \emph{Uspekhi Mat. Nauk}, 3:3(25) (1948), 29--112. (Russian)
  • Muskhelishvili, N.I., Singular integral equations. Boundary problems of function theory and their application to mathematical physics, Noordhoff International Publishing, Leyden, 1977.
  • Przeworska-Rolewicz, D. and Rolewicz, S., Equations in general spaces, Polish Scientific Publishers, Warsaw, 1968.
  • Simonenko, I.B., Riemann's boundary value problem with a continuous coefficient, Dokl. Akad. Nauk SSSR 124 (1959), 278--281. (in Russian)
  • Titchmarsh, E.C., Introduction to the Theory of Fourier Integrals, The Clarendon Press, Oxford University Press, New York, 1937.
  • Vekua, N.P., Systems of singular integral equations and some boundary value problems, Moscow (1970) (in Russian)
  • Yosida, K., Functional analysis Fourth edition. Die Grundlehren der mathematischen Wissenschaften, Band 123. Springer-Verlag, New York-Heidelberg, xii+496 pp. 1974.
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Review Articles
Authors

Beyaz Başak Koca 0000-0002-6481-6020

Nazım Sadık This is me 0000-0001-7105-7328

Publication Date February 1, 2019
Submission Date July 17, 2017
Acceptance Date May 29, 2018
Published in Issue Year 2019 Volume: 68 Issue: 1

Cite

APA Koca, B. B., & Sadık, N. (2019). A method for solving general singular equations and its application. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), 871-882. https://doi.org/10.31801/cfsuasmas.484955
AMA Koca BB, Sadık N. A method for solving general singular equations and its application. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2019;68(1):871-882. doi:10.31801/cfsuasmas.484955
Chicago Koca, Beyaz Başak, and Nazım Sadık. “A Method for Solving General Singular Equations and Its Application”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 1 (February 2019): 871-82. https://doi.org/10.31801/cfsuasmas.484955.
EndNote Koca BB, Sadık N (February 1, 2019) A method for solving general singular equations and its application. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 1 871–882.
IEEE B. B. Koca and N. Sadık, “A method for solving general singular equations and its application”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 1, pp. 871–882, 2019, doi: 10.31801/cfsuasmas.484955.
ISNAD Koca, Beyaz Başak - Sadık, Nazım. “A Method for Solving General Singular Equations and Its Application”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/1 (February 2019), 871-882. https://doi.org/10.31801/cfsuasmas.484955.
JAMA Koca BB, Sadık N. A method for solving general singular equations and its application. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:871–882.
MLA Koca, Beyaz Başak and Nazım Sadık. “A Method for Solving General Singular Equations and Its Application”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 1, 2019, pp. 871-82, doi:10.31801/cfsuasmas.484955.
Vancouver Koca BB, Sadık N. A method for solving general singular equations and its application. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(1):871-82.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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