Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2013, Article ID 607204, 20 pages
http://dx.doi.org/10.1155/2013/607204
Research Article

Some Bounded Linear Integral Operators and Linear Fredholm Integral Equations in the Spaces and

1İnönü Üniversitesi, Eğitim Fakültesi, A-Blok, Posta Kodu: 44280, Malatya, Turkey
2Baku State University, Department of Mech. & Math., Z. Khalilov Street, 23, P.O. Box 370145, Baku, Azerbaijan

Received 14 November 2012; Accepted 16 January 2013

Academic Editor: Juan Carlos Cortés López

Copyright © 2013 İsmet Özdemir et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. K. S. Thomas, “Galerkin methods for singular integral equations,” Mathematics of Computation, vol. 36, no. 153, pp. 193–205, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. T. Okayama, T. Matsuo, and M. Sugihara, “Sinc-collocation methods for weakly singular Fredholm integral equations of the second kind,” Journal of Computational and Applied Mathematics, vol. 234, no. 4, pp. 1211–1227, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. A. D. Polyanin and A. V. Manzhirov, Handbook of Integral Equations, CRC Press, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  4. P. K. Kythe and P. Puri, Computational Methods for Linear Integral Equations, Birkhäauser, Boston, Mass, USA, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  5. E. Babolian and A. A. Hajikandi, “The approximate solution of a class of Fredholm integral equations with a weakly singular kernel,” Journal of Computational and Applied Mathematics, vol. 235, no. 5, pp. 1148–1159, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. M. A. Abdou and A. A. Nasr, “On the numerical treatment of the singular integral equation of the second kind,” Applied Mathematics and Computation, vol. 146, no. 2-3, pp. 373–380, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. A. A. Badr, “Integro-differential equation with Cauchy kernel,” Journal of Computational and Applied Mathematics, vol. 134, no. 1-2, pp. 191–199, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. S. Bhattacharya and B. N. Mandal, “Numerical solution of a singular integro-differential equation,” Applied Mathematics and Computation, vol. 195, no. 1, pp. 346–350, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. M. R. Dostanić, “The asymptotic behavior of the singular values of the convolution operators with kernels whose Fourier transforms are rational functions,” Journal of Mathematical Analysis and Applications, vol. 395, no. 2, pp. 496–500, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. J. Diestel and J. J. Uhl, Jr., Vector Measures, Mathematical Surveys, No. 15, American Mathematical Society, Providence, RI, USA, 1979. View at MathSciNet
  11. R. F. Curtain and A. J. Pritchard, Functional Analysis in Modern Applied Mathematics, Academic Press, New York, NY, USA, 1977. View at MathSciNet
  12. B. D. Craven, Lebesgue measure & integral, Pitman, Toronto, Canada, 1982. View at MathSciNet
  13. C. Swartz, An Introduction to Functional Analysis, vol. 157 of Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, New York, NY, USA, 1992. View at MathSciNet
  14. R. Kress, Linear Integral Equations, vol. 82, Springer, Berlin, Germany, 1989. View at Publisher · View at Google Scholar · View at MathSciNet
  15. N. Dunford and J. T. Schwartz, Linear Operators Part III, Spectral Operators, John Wiley & Sons, New York, NY, USA, 1988. View at MathSciNet
  16. F. D. Gakhov and F. D., Kraevıe Zadaçi, 1963.
  17. N. L. Muskhelişvili, Singulyarnie Integralnie Uravneniya, Nauka, Moscow, Russia, 1968.
  18. T. G. Gegeliya, “Nekotorie Spesialnie Klassi Funksiy i ih Svoystva,” Tr. Tbilissk. Matem. in-Ta An Gruz SSR, vol. 32, pp. 94–139, 1966. View at Google Scholar