Weak contractive inequalities and compatible mixed monotone random operators in ordered metric spaces

*Correspondence: [email protected] 1Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia Full list of author information is available at the end of the article 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 (φ ,φ)-weak contractive conditions. These results present random versions and extensions of recent results of Ćirić 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.