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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 147409, 9 pages
http://dx.doi.org/10.1155/2013/147409
Research Article

The Existence and Attractivity of Solutions of an Urysohn Integral Equation on an Unbounded Interval

1Mathematics Department, Science Faculty for Girls, King Abdulaziz University, Jeddah, Saudi Arabia
2Department of Mathematics, Rzeszów University of Technology, al. Powstańców Warszawy 8, 35-959 Rzeszów, Poland
3Mathematics Depertment, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

Received 21 August 2013; Accepted 4 September 2013

Academic Editor: Mohammad Mursaleen

Copyright © 2013 Mohamed Abdalla Darwish 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. J. Banaś and K. Sadarangani, “Compactness conditions in the study of functional, differential, and integral equations,” Abstract and Applied Analysis, vol. 2013, Article ID 819315, 14 pages, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. K. Deimling, Nonlinear Functional Analysis, Springer, Berlin, Germany, 1985. View at MathSciNet
  3. M. A. Krasnosel'skii, P. P. Zabrejko, J. I. Pustylnik, and P. I. Sobolevskii, Integral Operators in Spaces of Summable Functions, Nordhoff, Leyden, Mass, USA, 1976.
  4. P. P. Zabrejko, A. I. Koshelev, M. A. Krasnosel'skii, S. G. Mikhlin, L. S. Rakovschik, and V. J. Stetsenko, Integral Equations, Nordhoff, Leyden, Mass, USA, 1975.
  5. I. J. Cabrera and K. B. Sadarangani, “Existence of solutions of a nonlinear integral equation on an unbounded interval,” Dynamic Systems and Applications, vol. 18, no. 3-4, pp. 551–570, 2009. View at Zentralblatt MATH · View at MathSciNet
  6. C. Corduneanu, Intergral Equations and Applications, Cambridge University Press, Cambridge, UK, 1991. View at Publisher · View at Google Scholar · View at MathSciNet
  7. N. Dunford and J. T. Schwartz, Linear Operators I, International Publishing, Leyden, The Netherlands, 1963. View at MathSciNet
  8. D. O'Regan and M. Meehan, Existence Theory for Nonlinear Integral and Integrodifferential Equations, Kluwer Academic, Dordrecht, The Netherlands, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  9. R. P. Agarwal, J. Banaś, K. Banaś, and D. O'Regan, “Solvability of a quadratic Hammerstein integral equation in the class of functions having limits at infinity,” Journal of Integral Equations and Applications, vol. 23, no. 2, pp. 157–181, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. J. Banaś and L. Olszowy, “On solutions of a quadratic Urysohn integral equation on an unbounded interval,” Dynamic Systems and Applications, vol. 17, no. 2, pp. 255–270, 2008. View at Zentralblatt MATH · View at MathSciNet
  11. M. A. Darwish and J. Henderson, “Nondecreasing solutions of a quadratic integral equation of Urysohn-Stieltjes type,” The Rocky Mountain Journal of Mathematics, vol. 42, no. 2, pp. 545–566, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. M. A. Darwish and K. Sadarangani, “Nondecreasing solutions of a quadratic Abel equation with supremum in the kernel,” Applied Mathematics and Computation, vol. 219, no. 14, pp. 7830–7836, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  13. M. Gil and S. Wedrychowicz, “Schauder-Tychonoff fixed-point theorem in the theory of superconductivity,” Journal of Function Spaces and Applications, vol. 2013, Article ID 692879, 12 pages, 2013. View at Publisher · View at Google Scholar
  14. L. Olszowy, “Fixed point theorems in the Fréchet space C(+) and functional integral equations on an unbounded interval,” Applied Mathematics and Computation, vol. 218, no. 18, pp. 9066–9074, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. L. Olszowy, “Nondecreasing solutions of a quadratic integral equation of Urysohn type on unbounded interval,” Journal of Convex Analysis, vol. 18, no. 2, pp. 455–464, 2011. View at Zentralblatt MATH · View at MathSciNet
  16. B. C. Dhage and V. Lakshmikantham, “On global existence and attractivity results for nonlinear functional integral equations,” Nonlinear Analysis: Theory, Methods & Applications A, vol. 72, no. 5, pp. 2219–2227, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. A. Aghajani and N. Sabzali, “Existence and local attractivity of solutions of a nonlinear quadratic functional integral equation,” Iranian Journal of Science and Technology, Transaction A, vol. 36, no. 4, pp. 453–460, 2012. View at Zentralblatt MATH · View at MathSciNet
  18. M. A. Darwish, “Monotonic solutions of a convolution functional-integral equation,” Applied Mathematics and Computation, vol. 219, no. 22, pp. 10777–10782, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  19. X. Hu and J. Yan, “The global attractivity and asymptotic stability of solution of a nonlinear integral equation,” Journal of Mathematical Analysis and Applications, vol. 321, no. 1, pp. 147–156, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. R. Stańczy, “Hammerstein equations with an integral over a noncompact domain,” Annales Polonici Mathematici, vol. 69, no. 1, pp. 49–60, 1998. View at Zentralblatt MATH · View at MathSciNet
  21. J. Banaś and K. Goebel, Measures of Noncompactness in Banach Spaces, vol. 60 of Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, New York, NY, USA, 1980. View at MathSciNet
  22. G. M. Fichtenholz, Differential and Integral Calculus, vol. 2, Wydawnictwo Naukowe PWN, Warsaw, Poland, 2007, (Polish).