International E-publication: Publish Projects, Dissertation, Theses, Books, Souvenir, Conference Proceeding with ISBN.  International E-Bulletin: Information/News regarding: Academics and Research

On Solutions of nonlinear functional integral equations in Frechet space

    , ,

Author Affiliations

  • 1Department of Mathematic, University of Benghazi, Libya
  • 2Department of Mathematics, Faculty of Education, University of Benghazi, Benghazi, Libya
  • 3College of Electrical and Electronic Technology, Benghazi, Libya

Res. J. Mathematical & Statistical Sci., Volume 11, Issue (1), Pages 1-3, May,12 (2023)

Abstract

In this article, a special type of integral equation will be investigated. The interest in this study to show existence of a unique solution on a semi-infinite interval in Frechet space by using a nonlinear alternative of the Leray-Schauder type for contraction maps.

References

  1. Arjunan, M.M. and Selvi, S. (2011)., Existence results for impulsive mixed Volterra-Fredholm integro differential inclusions with nonlocal conditions., Int. J. of math., 1(1), 101-119.
  2. Collins, P. J. (2006)., Differential and Integral Equations., OUP Oxford.
  3. Ibrahim, R. W. & Momani, S. (2007)., Upper and lower bounds of solutions for fractional integral equations., Surveys in Mathematics and its Applications, 2, 145-156.
  4. Pachpatte, B. G. (2008)., On a nonlinear Volterra-Fredholm integral equation., Sarajevo J. Math, 16, 61-71.
  5. Pachpatte, B. G. (2010)., Explicit estimates for some mixed integral inequalities., Electronic Journal of Differential Equations.
  6. Makhzoum, H., Elmabrok, A. S. & Elmansouri, R. (2021)., Existence and uniqueness of solutions for neutral periodic integro-differential equations with infinite delay on time scale., Caspian Journal of Mathematical Sciences, 10(1), 93-103.
  7. Makhzoum, H., Jalgaf, H., & Imhemed, A. (2021)., The existence and uniqueness of periodic solutions for nonlinear neutral dynamic equation with infinite delay on a Time Scale., International Journal of Scientific and Research Publications, 11(10), 389-396.
  8. Althubiti, S., Makhzoum, H. A. & Raffoul, Y. N. (2013)., Periodic solution and stability in nonlinear neutral system with infinite delay., Appl. Math. Sci, 7(136), 6749-6764.
  9. BenSaoud, I.F., Makhzoum, H.A., & Msaikc, K.M. (2021)., Existence of at least one positive continuing solution of Urysohn quadratic integral equation by Schauder fixed-point theorem., Libyan Journal of Science & Technology, 13(2), 112-115.
  10. Zeidler, E. (1985)., Nonlinear Functional Analysis and Its Applications I., Springer Verlag.
  11. Benchohra, M. & Darwish, M. A. (2010)., On quadratic integral equations of Urysohn type in Fréchet spaces., Acta Mathematica Universitatis Comenianae. New Series, 79(1), 105-110.
  12. Sadoon, L. H. (2014)., On Solutions of a Quadratic Integral Equation of Urysohn Type., Journal of Education and Science, 27(1), 92-96.