be a partially ordered set and suppose there is a metric
is a complete separable metric space and
be a measurable space. In this article, a pair of random mappings
has a mixed
-monotone property on
satisfy a certain nonlinear contractive condition, are introduced and investigated. Two coupled random coincidence and coupled random fixed point theorems are proved. These results are random versions and extensions of recent results of the authors [V. Lakshmikantham
and Lj. Ćirić, Nonlinear Anal., Theory Methods Appl. 70, No. 12 (A), 4341–4349 (2009; Zbl 1176.54032
)] and include several recent developments.