Volume 65 | Issue 3 | Year 2019 | Article Id. IJMTT-V65I3P528 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I3P528
In this work, we study the exitance of at least one and exactly one continuous or integrable solution of a functional integral equation with parameter. The continuous dependence of the unique solution on parameter and the function it self will be studied.
[1] Mohammed S Abdo and Satish K Panchal, E_ect of perturbation in the solution of fractional neutral functional di_erential equations, Journal of the Korean Society for Industrial and Applied Mathematics 22 (2018), no. 1, 63{74.
[2] Ravi P Agarwal, Bing Xu, and Weinian Zhang, Stability of functional equations in single variable, Journal of Mathematical Analysis and Applications 288 (2003), no. 2, 852{869.
[3] J_ozefBana_sandWagdyGomaa El-Sayed, Solvability of functional and integral equations in some classes of integrable functions, RedakcjaWydawnictwUczelnianychPolitechniki Rzeszowskiej, 1993.
[4] BelaidBouikhalene, The stability of some linear functional equations, J. Inequal. Pure Appl. Math 5 (2004), no. 2.
[5] KlausDeimling, Nonlinear functional analysis, Courier Corporation, 2010.
[6] Kazimierz Goebel and William A Kirk, Topics in metric _xed point theory, vol. 28, Cambridge University Press, 1990.
[7] Donald H Hyers, On the stability of the linear functional equation, Proceedings of the National Academy of Sciences of the United States of America 27 (1941), no. 4, 222.
[8] J Sousa and E Capelas de Oliveira, Existence, uniqueness, estimation and continuous dependence of the solutions of a nonlinear integral and an integrodi_erential equations of fractional order, arXiv preprint arXiv:1806.01441 (2018).
[9] Analytical Discussion for Existence of Idea of Calculus in Vedic and Post Vedic Periods, International Journal of MathematicsTrends and Technology, vol 61(6), 2018
A. M. A.El-Sayed, Muhanna.A.H. Alrashdi, "On the Continuous Dependence of a Functional Integral Equation with Parameter," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 3, pp. 183-189, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I3P528