Coupled Random Fixed Point Theorems for Nonlinear Contractions in Partially Ordered Metric Spaces

Let (X, ) be a partially ordered set and suppose there is a metric d on X such that (X, d) is a complete separable metric space and (, sigma) be a measurable space. In this article a pair of random mappings F: x(XxX)X and g: xXX, where F has a mixed g-monotone property on X, and F and g satisfy the non-linear contractive condition (5) below, 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 Lakshmikantham and Ciric [V. Lakshmikantham and Lj. Ciric, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces. Nonlinear Anal.Theor. 70(12) (2009): 4341-4349] and include several recent developments.