In this paper, we establish common fixed point theorems for two weakly compatible self-mappings satisfying the contractive condition or the quasi-contractive condition in the case of a quasi-contractive constant λ ∈ (0, 1/s) in cone b-metric spaces without the normal cone, where the coefficient s satisfies s ≥ 1. The main results generalize, extend and unify several well-known comparable results in the literature.

The aim of this work is to prove some coupled random coincidence theorems for a pair of compatible mixed monotone random operators satisfying weak contractive conditions. These results are some random versions and extensions of results of Karapınar et al. (2012). Our results generalize the results of Shatanawi and Mustafa (2012).