Coupled common fixed point results involving a ( φ , ψ ) -contractive condition for mixed g -monotone operators in partially ordered metric spaces

摘要

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 Appl. 2011:44, 2011), Bhaskar et al. (Nonlinear Anal. TMA 65:1379-1393, 2006), and Luong et al. (Nonlinear Anal. TMA 74:983-992, 2011). The effectiveness of the presented work is validated with the help of suitable examples. MSC:54H10, 54H25.