In this paper, we prove some coupled fixed point theorems for nonlinear contractive mappings which doesn't have the mixed monotone property, in the context of partially ordered `G`-metric spaces. Hence, these results can be applied in a much wider class of problems. Our results improve the result of D. Dori'{c}, Z. Kadelburg and S. Radenovi'{c} [Appl. Math. Lett. (2012)]. We also present two examples to support these new results.

Keywords: `G`-metric space, coupled common fixed point, mixed monotone property

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