Coupled coincidence point theorems for ?-contractive under (f, g)-invariant set in complete metric space

In this paper, we prove existence of a coupled coincidence point theorem and coupled common fixed point theorem for φ-contractive mappings in partially ordered complete metric space without the mixed g-monotone property by using the concept of an (F, g)-invariant set. We prove some coupled fixed point theorems for such nonlinear contractive mappings in a complete metric space.Our results are generalization of the results of Wutiphol Sintunavarat, Poom Kumam and Yeol Je Cho (Coupled fixed point theorems for nonlinear contractions without mixed monotone property, Fixed Point Theory and Applications 2012,2012:170.).