Coupled fixed point results for mappings involving weak contractions in ordered metric spaces and applications

In this paper we introduce the notion of ??,?? - weak contractions and use the notion to establish the existence and uniqueness of coupled common fixed points for the mixed monotone operators in partially ordered metric spaces. The obtained results extend, improve, complement and unify many recent coupled fixed point results present in the literature. The theoretic results are accompanied with suitable examples. An application to the existence and uniqueness of the solution of the system of integral equations is also presented.