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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 46 | Number 4 | Year 2017 | Article Id. IJMTT-V46P539 | DOI : https://doi.org/10.14445/22315373/IJMTT-V46P539

Existence and uniqueness for Volterra nonlinear integral equation


Faez N. Ghaffoori
Abstract

We study the existence and uniqueness theorem of a functional Volterra integral equation in the space of Lebesgue integrable on unbounded interval by using the Banach fixed point theorem.

Keywords
Superposition operator-Nonlinear Volterra integral functional equation-Banach fixed point theorem- Lipschitz condition.
References

[1] M. M. El-Borai, Wagdy G. El-Sayed and Faez N. Ghaffoori, On The Solvability of Nonlinear Integral Functional Equation, (IJMTT) Vo 34, No. 1, June 2016.
[2] P. P. Zarejko, A.I. Koshlev, M. A. Krasnoselskii, S. G. Mikhlin, L. S. Rakovshchik, V. J. Stecenko, Integral Equations, Noordhoff, Leyden, 1975.
[3] J. Appell and P. P. Zabroejko, Continuity properties of the superposition operator, No. 131, Univ. Augsburg, (1986).
[4] M. M. A. Metwali, On solutions of quadratic integral equations, Adam Mickiewicz University (2013).
[5] J. Bana's and W. G. El-Sayed, Solvability of functional and Integral Equations in some classes of integrable functions, 1993.
[6] J. Appell and P. P. Zabroejko, Continuity properties of the superposition operator, No. 131, Univ. Augsburg, (1986). [7] R. R. Van Hassel, Functional Analysis, December 16, (2004).
[8] I. G. Petrovski and R. A .Silverman, Ordinary Differential Equations, 1973.
[9] Ravi P. Agarwal, Maria Meehan and Donal O'regan, Fixed Point Theory and Applications Cambridge University Press, 2004.

Citation :

Faez N. Ghaffoori, "Existence and uniqueness for Volterra nonlinear integral equation," International Journal of Mathematics Trends and Technology (IJMTT), vol. 46, no. 4, pp. 272-276, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V46P539

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