Extension of Darbo fixed-point theorem to illustrate existence of the solutions of some nonlinear functional stochastic integral equations

In this paper, Darbo fixed-point theorem is employed as a mathematical tool to examine existence of the solution of some nonlinear functional stochastic integral equations which arise in many physical, chemical and biological problems. Throughout this paper, we consider (C[۰, ۱]; ∥.∥ ) as Banach space equipped with uniform norm.

Keywords:

Nonlinear functional integral equations , Stochastic integral equations , Fixed-point theorem , Banach space , Measure of non-compactness