Existence of Solutions of Nonlinear Stochastic Volterra Fredholm Integral Equations of Mixed Type

Random or stochastic integral equations are important in the study of many physical phenomena in life sciences, engineering, and technology 1–13 . Currently there are two basic versions of stochastic integral equations being studied bymathematical statisticians and probabilists namely, those integral equations involving Ito-Doob type of stochastic integrals and those which can be formed as probabilistic analogues of classical deterministic integral equations whose formulation involves the usual Lebesgue integral. Equations of the later category have been studied extensively by several authors 4, 10, 14–40 . Many papers have been appeared on the problem of existence of solutions of nonlinear random integral equations and the results are established by applying various fixed point techniques. These methods are broadly classified into three categories: