(H, F)-Closed set and coupled coincidence point theorems for a generalized compatible in partially G-metric spaces.

In this work, we present a notion of an (H, F)-closed set and prove the existence of a coupled coincidence point theorem for a pair {F,H} of mappings F,H : X × X → X with ϕ-contraction mappings in partially ordered metric spaces without H-increasing property of F and mixed monotone property of H. We give some examples of a nonlinear contraction mapping, which is not applied to the existence of coupled coincidence point by H using the mixed monotone property and H-increasing property of F. We also show the uniqueness of a coupled coincidence point of the given mappings. Further, we apply our results to the existence and uniqueness of a coupled coincidence point of the given mappings in partially ordered G-metric spaces with H-increasing property of F and mixed monotone property of H. These results generalize some recent results in the literature. [ABSTRACT FROM AUTHOR]