Abstract
AbstractThe contraction condition in the Banach contraction principle
forces a function to be continuous. Many authors overcome this obligation and
weaken the hypotheses via metric spaces endowed with a partial order. In this paper,
we present some coupled fixed point theorems for the functions having mixed
monotone properties on ordered vector metric spaces, which are more general
spaces than partially ordered metric spaces. We also define the double monotone
property and investigate the previous results with this property. In the last
section, we prove the uniqueness of a coupled fixed point for non-monotone functions.
In addition, we present some illustrative examples to emphasize that our
results are more general than the ones in the literature.
Publisher
Springer Science and Business Media LLC