We establish coincidence point theorem for g-non-decreasing mappings under generalized (ψ, θ, φ)-contraction on partially ordered metric spaces. With the help of the obtain result, we indicate the formation of a coupled coincidence point theorem of generalized compatible pair of mappings F,G: X2 → X. We apply our result to obtain the solution of integral equation and also give an example to show the degree of validity of our hypothesis. Our results modify, improve, sharpen, enrich and generalize various known results. © 2021 by TJM.