Existence theory for first order functional random integrodifferential inclusions

Abstract

In this paper, some existence theorems for a first   order ordinary functional random integrodifferential inclusion  are proved for convex and nonconvex cases of random multi-valued functions involved in the inclusion. The existence theorems for extremal random solutions are also proved under certain monotonicity conditions of the multi-valued function. The  multi-valued random fixed point theoretic approach of Dhage (1907,1911) is used while establishing the main results of this paper.