On random fixed point theorems with applications to integral equations

This particular research establishes some random fixed point theorems for general nonlinear random contractive operators in the context of partially ordered separable metric spaces. The existence and uniqueness of the random solution for the nonlinear integral equation is obtained by applying the result of the random fixed point. The results generalize and improve on some related works in the literature. • Our theorems are proved in the context of metric space while Saluja and Tripathi [8] proved in the context of partial metric spaces. • Nieto, Ouahab and. Rodriguez-Lopez [9] proved their theorem using Banach contraction mappings while we proved our theorems using Hardy and Rogers contraction mappings. • Rashwan and Albaqeri [3] proved the solution of the random integral equation using the Banach contraction operator while we proved our solution to the random integral equations employing more general contractive operator.