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

Narawadee Na Nan, Phakdi Charoensawan
2014 Journal of Inequalities and Applications  
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
more » ... 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.
doi:10.1186/1029-242x-2014-342 fatcat:vfm5dbfro5aidmu6r32lbrqnpu