Coupled g-coincidence point theorems for a generalized compatible pair in complete metric spaces

In this work, we give the notions of coupled g-coincidence point and H-g-increasing property of F for mappings F, H : X x X -> X and g : X -> X and prove the existence and uniqueness of a coupled g-coincidence point theorem for mappings F, H : X x X -> X and g : X -> X with phi-contraction mappings in complete metric spaces without the H-g-increasing property of F and the mixed monotone property of G. Further, we apply our results to the existence and uniqueness of a coupled g-coincidence point of the given mappings with the H-g-increasing property of F and the mixed monotone property of H in partially ordered metric spaces.