We study the existence, uniqueness, and stability of random solutions of a general class of nonlinear stochastic integral equations by using the Banach fixed point theorem. The results obtained in this paper generalize the results of Szynal and Wędrychowicz (1993).
K. Balachandran, K. Sumathy, and H. H. Kuo, “Existence of solutions of general nonlinear stochastic Volterra Fredholm integral equations,” Stochastic Analysis and Applications, vol. 23, no. 4, pp. 827–851, 2005.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetJ. Banaś, D. Szynal, and S. Wędrychowicz, “On existence, asymptotic behaviour and stability of solutions of stochastic integral equations,” Stochastic Analysis and Applications, vol. 9, no. 4, pp. 363–385, 1991.
View at: Google Scholar | Zentralblatt MATH | MathSciNetA. T. Bharucha-Reid, Random Integral Equations, vol. 96 of Mathematics in Science and Engineering, Academic Press, New York, 1972.
View at: Google Scholar | Zentralblatt MATH | MathSciNetH. Gacki, T. Szarek, and S. Wędrychowicz, “On existence, and stability of solutions of stochastic integral equations,” Indian Journal of Pure and Applied Mathematics, vol. 29, no. 2, pp. 175–189, 1998.
View at: Google Scholar | Zentralblatt MATH | MathSciNetS. T. Hardiman and C. P. Tsokos, “Existence and stability behavior of random solutions of a system of nonlinear random equations,” Information Sciences, vol. 9, no. 4, pp. 299–313, 1975.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetJ. S. Milton, W. J. Padgett, and C. P. Tsokos, “On the existence and uniqueness of a random solution to a perturbed random integral equation of the Fredholm type,” SIAM Journal on Applied Mathematics, vol. 22, pp. 194–208, 1972.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetW. J. Padgett, “On non-linear perturbations of stochastic Volterra integral equations,” International Journal of Systems Science, vol. 4, pp. 795–802, 1973.
View at: Google Scholar | Zentralblatt MATH | MathSciNetA. N. V. Rao and C. P. Tsokos, “On the existence of a random solution to a nonlinear perturbed stochastic integral equation,” Annals of the Institute of Statistical Mathematics, vol. 28, no. 1, pp. 99–109, 1976.
View at: Google Scholar | Zentralblatt MATH | MathSciNetA. N. V. Rao and C. P. Tsokos, “Existence and boundedness of random solutions to stochastic functional integral equations,” Acta Mathematica Academiae Scientiarum Hungaricae, vol. 29, no. 3-4, pp. 283–288, 1977.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetR. Subramaniam and K. Balachandran, “Existence of solutions of general nonlinear stochastic integral equations,” Indian Journal of Pure and Applied Mathematics, vol. 28, no. 6, pp. 775–789, 1997.
View at: Google Scholar | Zentralblatt MATH | MathSciNetR. Subramaniam and K. Balachandran, “Existence of solutions of a class of stochastic Volterra integral equations with applications to chemotherapy,” Journal of Australian Mathematical Society. Series B. Applied Mathematics, vol. 41, no. 1, pp. 93–104, 1999.
View at: Google Scholar | Zentralblatt MATH | MathSciNetD. Szynal and S. Wędrychowicz, “On existence and asymptotic behaviour of solutions of a nonlinear stochastic integral equation,” Annali di Matematica Pura ed Applicata. Serie Quarta, vol. 142, pp. 105–119 (1986), 1985.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetD. Szynal and S. Wędrychowicz, “On existence and an asymptotic behavior of random solutions of a class of stochastic functional-integral equations,” Colloquium Mathematicum, vol. 51, pp. 349–364, 1987.
View at: Google Scholar | Zentralblatt MATH | MathSciNetD. Szynal and S. Wędrychowicz, “On solutions of a stochastic integral equation of the Volterra type with applications for chemotherapy,” Journal of Applied Probability, vol. 25, no. 2, pp. 257–267, 1988.
View at: Google Scholar | Zentralblatt MATH | MathSciNetD. Szynal and S. Wędrychowicz, “On solutions of some nonlinear stochastic integral equations,” Yokohama Mathematical Journal, vol. 41, no. 1, pp. 31–37, 1993.
View at: Google Scholar | Zentralblatt MATH | MathSciNetC. P. Tsokos and W. J. Padgett, Random Integral Equations with Applications to Life Sciences and Engineering, vol. 108 of Mathematics in Science and Engineering, Academic Press, New York, 1974.
View at: Google Scholar | Zentralblatt MATH | MathSciNet