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In this work, we show the existence of a coupled coincidence point and a coupled common fixed point for a ϕ-contractive mapping in G-metric spaces without the mixed g-monotone property, using the concept of a (F∗,g)-invariant set. We also show the uniqueness of a coupled coincidence point and give some examples, which are not applied to the existence of a coupled coincidence point by using the mixed g-monotone property. Further, we apply our results to the existence and uniqueness of a coupled coincidence point of the given mapping in partially ordered G-metric spaces.

Coupled coincidence point theorems for a ϕ-contractive mapping in partially ordered G-metric spaces without mixed g-monotone property