The aim of this paper is to extend the notions of E.A. property andCLRgproperty for coupled mappings and use these notions to generalize the recent results of Xin-Qi Hu (2011). The main result is supported by a suitable example.

In the setting of partially ordered metric spaces, using the notion of compatible mappings, we establish the existence and uniqueness of coupled common fixed points involving a (ϕ, ψ)-contractive condition for mixed g-monotone operators. Our results extend and generalize the well-known results of Berinde (Nonlinear Anal. TMA 74:7347-7355, 2011; Nonlinear Anal. TMA 75:3218-3228, 2012) and weaken the contractive conditions involved in the results of Alotaibi et al. (Fixed Point Theory

The aim of this paper is to establish some common fixed point theorems under occasionally weakly compatible maps using implicit functions.

The object of this paper is to establish the existence and uniqueness of coupled fixed points under a (φ, ψ)-contractive condition for mixed monotone operators in the setup of partially ordered metric spaces. Presented work generalizes the recent results of Berinde (2011, 2012) and weakens the contractive conditions involved in the well-known results of Bhaskar and Lakshmikantham (2006), and Luong and Thuan (2011). The effectiveness of our work is validated with the help of a suitable example. As an application, we give a result of existence and uniqueness for the solutions of a class of nonlinear integral equations.

We establish some coupled coincidence and coupled common fixed point theorems for the mixed g-monotone mappings satisfying (φ, ψ)-contractive conditions in the setting of ordered generalized metric spaces. Presented theorems extend and generalize the very recent results of Choudhury and Maity (Math. Comput. Model. 54(1-2):73-79, 2011). To illustrate our results, an example and an application to integral equations have also been given. MSC: 54H10; 54H25