SavedAdd your journal

Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 68 Issue: 1

A method for solving general singular equations and its application

Beyaz Başak Koca0000-0002-6481-6020
Nazım Sadık0000-0001-7105-7328
Pages
—
Publication Date
2019-02-01
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

As an application of this method, we give a solution for a class of convolution-type integral equations

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper we present a new method for solving general singular equations of normal type.
📊
Key Findings & Data:In this paper we present a new method for solving general singular equations of normal type.
💡
Conclusion & Impact:As an application of this method, we give a solution for a class of convolution-type integral equations
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Integral equations · singular integral equations · convolution type integral equation

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

🔖

Cite This Article

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, Volume: 68 Issue: 1. https://doi.org/10.31801/cfsuasmas.484955

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (15)

  1. Atkinson, F.V., The normal solubility of linear equations in normed spaces, Mat. Sbornik N.S. 28(70) (1951), 3--14. (in Russian)
  2. Cherskii, Yu.I., The general singular equation and equations of convolution type, Mat.Sb.N.S., 41(83):3 (1957), 277--296. (in Russian)
  3. Gakhov, F.D., Boundary Value Problems, Pergamon Press, Oxford-New York-Paris; Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1966.
  4. 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)
  5. Halmos, P.R., A Hilbert Space Problem Book, Springer-Verlag, Berlin-New York, 1978.
  6. Helemskii, A.Y., Lectures and Exercises on Functional Analysis, Moscow State University; AMS, Vol.233, 2006.
  7. Khalilov, Z. I., Linear singular equations in a normed ring, Izvestiya Akad. Nauk SSSR. Ser. Mat. 13 (1949), 163--176. (in Russian)
  8. 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)
  9. Muskhelishvili, N.I., Singular integral equations. Boundary problems of function theory and their application to mathematical physics, Noordhoff International Publishing, Leyden, 1977.
  10. Przeworska-Rolewicz, D. and Rolewicz, S., Equations in general spaces, Polish Scientific Publishers, Warsaw, 1968.
  11. Simonenko, I.B., Riemann's boundary value problem with a continuous coefficient, Dokl. Akad. Nauk SSSR 124 (1959), 278--281. (in Russian)
  12. Titchmarsh, E.C., Introduction to the Theory of Fourier Integrals, The Clarendon Press, Oxford University Press, New York, 1937.
  13. Vekua, N.P., Systems of singular integral equations and some boundary value problems, Moscow (1970) (in Russian)
  14. Yosida, K., Functional analysis Fourth edition. Die Grundlehren der mathematischen Wissenschaften, Band 123. Springer-Verlag, New York-Heidelberg, xii+496 pp. 1974.
  15. 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)