Coupled fixed point results for new classes of functions on ordered vector metric space

The contraction condition in the Banach contraction principleforces a function to be continuous. Many authors overcome this obligation andweaken the hypotheses via metric spaces endowed with a partial order. In this paper,we present some coupled fixed point theorems for the functions having mixedmonotone properties on ordered vector metric spaces, which are more generalspaces than partially ordered metric spaces. We also define the double monotoneproperty and investigate the previous results with this property. In the lastsection, we prove the uniqueness of a coupled fixed point for non-monotone functions.In addition, we present some illustrative examples to emphasize that ourresults are more general than the ones in the literature.