SOLUTIONS FOR A SYSTEM OF RANDOM OPERATOR EQUATIONS AND SOME APPLICATIONS

Abstract

The present paper is a continuation of [1]. By using more general type of random contractor than that defined by Lee and Padgett, we show several existence and uniqueness theorems for solutions to a system of nonlinear random operator equations with stochastic domain. Next, we obtain a random coincidence theorem and a random implicit function theorem, which improves and generalizes the corresponding results of Ding, Reddy and Subrahmanyam, Altman, Eng, Krasnoselskii and others. Finally, some applications of our results are given for the solutions of a system of nonlinear random integral equations.