Abstract
The aim of this work is to define the notion of compatible random operators in a partially ordered metric space and prove some coupled random coincidence theorems for a pair of compatible mixed monotone random operators satisfying (phi, phi)-weak contractive conditions. These results present random versions and extensions of recent results of Ciric and Lakshmikantham (Stoch. Anal. Appl. 27: 1246-1259, 2009), Choudhury and Kundu (Nonlinear Anal. 73: 2524-2531, 2010), Alotaibi and Alsulami (Fixed Point Theory Appl. 2011: 44, 2011) and many others.