The present paper studies the random versions of some deterministic fixed point theorems of Dhage [5] and Dhage and Regon [7]. Applications are given to a certain nonlinear functional random integral equation for proving the existence of random solution under the generalized Lipschitzicity and Caratheodory conditions.

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In this paper some algebraic and topological random fixed point theorems are proved involving the three random operators on a Banach algebra and they are further applied to a certain nonlinear functional random integral equation of mixed type for proving the existence as well as existence of extremal random solutions under the generalized Lipschizicity, Carath´eodory and monotonicity conditions.

In this paper the existence as well as the existence of the extremal solutions for first order nonlinear perturbed functional random differential equations is proved under mixed Lipschitz, compactness and monotonic conditions.

In this paper a random version of a fixed-point theorem of Schaefer is obtained and it is further applied to a certain nonlinear functional random integral equation for proving the existence result under Caratheodory conditions.