Abstract
In this paper we discuss a coupled fixed point problem formulated with respect to \(w\) -distances which are additional distance functions defined on metric spaces. This concept has been utilized in recent literature for extending many results of the metric fixed point theory. We establish a coupled fixed point theorem using a Pata-type inequality with respect to \(w\) -distances. There is a corollary which is a \(w\) -distance version of the coupled contraction mapping theorem. We have one application to a system of integral equations and certain results in the special case where \(w\) -distance is the metric function. One illustration is discussed through which we indicate the utility of treating \(w\) -distances in fixed point theory.
